Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfaltop Structured version   Visualization version   GIF version

Theorem nfaltop 32424
 Description: Bound-variable hypothesis builder for alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.)
Hypotheses
Ref Expression
nfaltop.1 𝑥𝐴
nfaltop.2 𝑥𝐵
Assertion
Ref Expression
nfaltop 𝑥𝐴, 𝐵

Proof of Theorem nfaltop
StepHypRef Expression
1 df-altop 32402 . 2 𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}}
2 nfaltop.1 . . . 4 𝑥𝐴
32nfsn 4379 . . 3 𝑥{𝐴}
4 nfaltop.2 . . . . 5 𝑥𝐵
54nfsn 4379 . . . 4 𝑥{𝐵}
62, 5nfpr 4369 . . 3 𝑥{𝐴, {𝐵}}
73, 6nfpr 4369 . 2 𝑥{{𝐴}, {𝐴, {𝐵}}}
81, 7nfcxfr 2911 1 𝑥𝐴, 𝐵
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2900  {csn 4316  {cpr 4318  ⟪caltop 32400 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-un 3728  df-sn 4317  df-pr 4319  df-altop 32402 This theorem is referenced by:  sbcaltop  32425
 Copyright terms: Public domain W3C validator