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Theorem recseq 6637
 Description: Equality theorem for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.)
Assertion
Ref Expression
recseq recs recs

Proof of Theorem recseq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq1 5730 . . . . . . . 8
21eqeq2d 2449 . . . . . . 7
32ralbidv 2727 . . . . . 6
43anbi2d 686 . . . . 5
54rexbidv 2728 . . . 4
65abbidv 2552 . . 3
76unieqd 4028 . 2
8 df-recs 6636 . 2 recs
9 df-recs 6636 . 2 recs
107, 8, 93eqtr4g 2495 1 recs recs
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653  cab 2424  wral 2707  wrex 2708  cuni 4017  con0 4584   cres 4883   wfn 5452  cfv 5457  recscrecs 6635 This theorem is referenced by:  rdgeq1  6672  rdgeq2  6673  dfoi  7483  oieq1  7484  oieq2  7485  ordtypecbv  7489  dfac12r  8031  zorn2g  8388  ttukey2g  8401  aomclem3  27145  aomclem8  27150 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 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-recs 6636
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