Theorem op1sta 5397

Description: Extract the first member of an ordered pair. (See op2nda 5400 to extract the second member, op1stb 4799 for an alternate version, and op1st 6405 for the preferred version.) (Contributed by Raph Levien, 4-Dec-2003.)

Hypotheses

Ref	Expression
cnvsn.1
cnvsn.2

Assertion

Ref	Expression
op1sta

Proof of Theorem op1sta

Step	Hyp	Ref	Expression
1		cnvsn.2	. . . 4
2	1	dmsnop 5390	. . 3
3	2	unieqi 4052	. 2
4		cnvsn.1	. . 3
5	4	unisn 4058	. 2
6	3, 5	eqtri 2463	1

Syntax hints:  =wceq 1654  e.wcel 1728  cvv 2965  {csn 3841  <.cop 3844  U.cuni 4043  domcdm 4919

This theorem is referenced by:  elxp4  5403  op1st  6405  fo1st  6416  f1stres  6418  xpassen  7251  xpdom2  7252

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4364  ax-nul 4372  ax-pr 4442

This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-rex 2718  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850  df-uni 4044  df-br 4244  df-dm 4929