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Theorem recseq 6085
 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 5317 . . . . . . . 8
21eqeq2d 2100 . . . . . . 7
32ralbidv 2381 . . . . . 6
43anbi2d 453 . . . . 5
54rexbidv 2382 . . . 4
65abbidv 2206 . . 3
76unieqd 3670 . 2
8 df-recs 6084 . 2 recs
9 df-recs 6084 . 2 recs
107, 8, 93eqtr4g 2146 1 recs recs
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1290  cab 2075  wral 2360  wrex 2361  cuni 3659  con0 4199   cres 4454   wfn 5023  cfv 5028  recscrecs 6083 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-uni 3660  df-br 3852  df-iota 4993  df-fv 5036  df-recs 6084 This theorem is referenced by:  rdgeq1  6150  rdgeq2  6151  freceq1  6171  freceq2  6172  frecsuclem  6185
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