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Theorem recseq 7357
 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 7299 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 7355 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 7355 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2669 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   E cep 4947  Oncon0 5640  wrecscwrecs 7293  recscrecs 7354 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-xp 5044  df-cnv 5046  df-dm 5048  df-rn 5049  df-res 5050  df-ima 5051  df-pred 5597  df-iota 5768  df-fv 5812  df-wrecs 7294  df-recs 7355 This theorem is referenced by:  rdgeq1  7394  rdgeq2  7395  dfoi  8299  oieq1  8300  oieq2  8301  ordtypecbv  8305  dfac12r  8851  zorn2g  9208  ttukey2g  9221  csbrdgg  32351  aomclem3  36644  aomclem8  36649
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