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Theorem recseq 8414
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 8345 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 8411 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 8411 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2802 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540   E cep 5583  Oncon0 6384  wrecscwrecs 8336  recscrecs 8410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-xp 5691  df-cnv 5693  df-co 5694  df-dm 5695  df-rn 5696  df-res 5697  df-ima 5698  df-pred 6321  df-iota 6514  df-fv 6569  df-ov 7434  df-frecs 8306  df-wrecs 8337  df-recs 8411
This theorem is referenced by:  rdgeq1  8451  rdgeq2  8452  dfoi  9551  oieq1  9552  oieq2  9553  ordtypecbv  9557  dfac12r  10187  zorn2g  10543  ttukey2g  10556  csbrdgg  37330  aomclem3  43068  aomclem8  43073
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