MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  6p4e10OLD Structured version   Visualization version   GIF version

Theorem 6p4e10OLD 11372
Description: 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 6p4e10 11798 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
6p4e10OLD (6 + 4) = 10

Proof of Theorem 6p4e10OLD
StepHypRef Expression
1 df-4 11282 . . . 4 4 = (3 + 1)
21oveq2i 6803 . . 3 (6 + 4) = (6 + (3 + 1))
3 6cn 11303 . . . 4 6 ∈ ℂ
4 3cn 11296 . . . 4 3 ∈ ℂ
5 ax-1cn 10195 . . . 4 1 ∈ ℂ
63, 4, 5addassi 10249 . . 3 ((6 + 3) + 1) = (6 + (3 + 1))
72, 6eqtr4i 2795 . 2 (6 + 4) = ((6 + 3) + 1)
8 df-10OLD 11288 . . 3 10 = (9 + 1)
9 6p3e9 11371 . . . 4 (6 + 3) = 9
109oveq1i 6802 . . 3 ((6 + 3) + 1) = (9 + 1)
118, 10eqtr4i 2795 . 2 10 = ((6 + 3) + 1)
127, 11eqtr4i 2795 1 (6 + 4) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1630  (class class class)co 6792  1c1 10138   + caddc 10140  3c3 11272  4c4 11273  6c6 11275  9c9 11278  10c10 11279
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-resscn 10194  ax-1cn 10195  ax-icn 10196  ax-addcl 10197  ax-addrcl 10198  ax-mulcl 10199  ax-mulrcl 10200  ax-addass 10202  ax-i2m1 10205  ax-1ne0 10206  ax-rrecex 10209  ax-cnre 10210
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ne 2943  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-uni 4573  df-br 4785  df-iota 5994  df-fv 6039  df-ov 6795  df-2 11280  df-3 11281  df-4 11282  df-5 11283  df-6 11284  df-7 11285  df-8 11286  df-9 11287  df-10OLD 11288
This theorem is referenced by:  6p4e10bOLD  11799  6p5e11OLD  11801  6t5e30OLD  11845
  Copyright terms: Public domain W3C validator