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Theorem recseq 7331
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 7273 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 7329 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 7329 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2665 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1474   E cep 4934  Oncon0 5623  wrecscwrecs 7267  recscrecs 7328
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2032  ax-13 2229  ax-ext 2586
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2593  df-cleq 2599  df-clel 2602  df-nfc 2736  df-ral 2897  df-rex 2898  df-rab 2901  df-v 3171  df-dif 3539  df-un 3541  df-in 3543  df-ss 3550  df-nul 3871  df-if 4033  df-sn 4122  df-pr 4124  df-op 4128  df-uni 4364  df-br 4575  df-opab 4635  df-xp 5031  df-cnv 5033  df-dm 5035  df-rn 5036  df-res 5037  df-ima 5038  df-pred 5580  df-iota 5751  df-fv 5795  df-wrecs 7268  df-recs 7329
This theorem is referenced by:  rdgeq1  7368  rdgeq2  7369  dfoi  8273  oieq1  8274  oieq2  8275  ordtypecbv  8279  dfac12r  8825  zorn2g  9182  ttukey2g  9195  csbrdgg  32151  aomclem3  36444  aomclem8  36449
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