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Theorem recseq 7993
 Description: Equality theorem for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.)
Assertion
Ref Expression
recseq (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))

Proof of Theorem recseq
StepHypRef Expression
1 wrecseq3 7935 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 7991 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 7991 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2858 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   E cep 5429  Oncon0 6159  wrecscwrecs 7929  recscrecs 7990 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rab 3115  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-opab 5093  df-xp 5525  df-cnv 5527  df-dm 5529  df-rn 5530  df-res 5531  df-ima 5532  df-pred 6116  df-iota 6283  df-fv 6332  df-wrecs 7930  df-recs 7991 This theorem is referenced by:  rdgeq1  8030  rdgeq2  8031  dfoi  8959  oieq1  8960  oieq2  8961  ordtypecbv  8965  dfac12r  9557  zorn2g  9914  ttukey2g  9927  csbrdgg  34746  aomclem3  39998  aomclem8  40003
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