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Theorem recseq 8361
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 8292 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 8358 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 8358 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2798 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542   E cep 5575  Oncon0 6356  wrecscwrecs 8283  recscrecs 8357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3063  df-rab 3434  df-v 3477  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-nul 4321  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4905  df-br 5145  df-opab 5207  df-xp 5678  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-ima 5685  df-pred 6292  df-iota 6487  df-fv 6543  df-ov 7399  df-frecs 8253  df-wrecs 8284  df-recs 8358
This theorem is referenced by:  rdgeq1  8398  rdgeq2  8399  dfoi  9493  oieq1  9494  oieq2  9495  ordtypecbv  9499  dfac12r  10128  zorn2g  10485  ttukey2g  10498  csbrdgg  36115  aomclem3  41669  aomclem8  41674
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