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Theorem op1sta 5020
 Description: Extract the first member of an ordered pair. (See op2nda 5023 to extract the second member and op1stb 4399 for an alternate 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 5012 . . 3 dom {⟨𝐴, 𝐵⟩} = {𝐴}
32unieqi 3746 . 2 dom {⟨𝐴, 𝐵⟩} = {𝐴}
4 cnvsn.1 . . 3 𝐴 ∈ V
54unisn 3752 . 2 {𝐴} = 𝐴
63, 5eqtri 2160 1 dom {⟨𝐴, 𝐵⟩} = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ∈ wcel 1480  Vcvv 2686  {csn 3527  ⟨cop 3530  ∪ cuni 3736  dom cdm 4539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-dm 4549 This theorem is referenced by:  op1st  6044  fo1st  6055  f1stres  6057  xpassen  6724  xpdom2  6725
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