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Theorem prexgOLD 3946
 Description: The Axiom of Pairing using class variables. Theorem 7.13 of [Quine] p. 51, but restricted to classes which exist. For proper classes, see prprc 3480, prprc1 3478, and prprc2 3479. This is a special case of prexg 3947 and new proofs should use prexg 3947 instead. (Contributed by Jim Kingdon, 25-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.) TODO: replace its uses by uses of prexg 3947 and then remove it.
Assertion
Ref Expression
prexgOLD

Proof of Theorem prexgOLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 preq2 3448 . . . . . 6
21eleq1d 2106 . . . . 5
3 zfpair2 3945 . . . . 5
42, 3vtoclg 2613 . . . 4
5 preq1 3447 . . . . 5
65eleq1d 2106 . . . 4
74, 6syl5ib 143 . . 3
87vtocleg 2624 . 2
98imp 115 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  cvv 2557  cpr 3376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  prelpwi  3950  opexgOLD  3965  opi2  3970  opth  3974  opeqsn  3989  opeqpr  3990  uniop  3992  unex  4176  op1stb  4209  op1stbg  4210  opthreg  4280  relop  4486
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