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Theorem op1sta 5760
Description: Extract the first member of an ordered pair. (See op2nda 5764 to extract the second member, op1stb 5067 for an alternate version, and op1st 7322 for the preferred version.) (Contributed by Raph Levien, 4-Dec-2003.)
Hypotheses
Ref Expression
cnvsn.1 𝐴 ∈ V
cnvsn.2 𝐵 ∈ V
Assertion
Ref Expression
op1sta dom {⟨𝐴, 𝐵⟩} = 𝐴

Proof of Theorem op1sta
StepHypRef Expression
1 cnvsn.2 . . . 4 𝐵 ∈ V
21dmsnop 5751 . . 3 dom {⟨𝐴, 𝐵⟩} = {𝐴}
32unieqi 4581 . 2 dom {⟨𝐴, 𝐵⟩} = {𝐴}
4 cnvsn.1 . . 3 𝐴 ∈ V
54unisn 4587 . 2 {𝐴} = 𝐴
63, 5eqtri 2792 1 dom {⟨𝐴, 𝐵⟩} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1630  wcel 2144  Vcvv 3349  {csn 4314  cop 4320   cuni 4572  dom cdm 5249
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-sep 4912  ax-nul 4920  ax-pr 5034
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-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-dm 5259
This theorem is referenced by:  elxp4  7256  op1st  7322  fo1st  7334  f1stres  7338  xpassen  8209  xpdom2  8210
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