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Theorem recseq 8413
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 8344 . 2 (𝐹 = 𝐺 → wrecs( E , On, 𝐹) = wrecs( E , On, 𝐺))
2 df-recs 8410 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
3 df-recs 8410 . 2 recs(𝐺) = wrecs( E , On, 𝐺)
41, 2, 33eqtr4g 2800 1 (𝐹 = 𝐺 → recs(𝐹) = recs(𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537   E cep 5588  Oncon0 6386  wrecscwrecs 8335  recscrecs 8409
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-co 5698  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-pred 6323  df-iota 6516  df-fv 6571  df-ov 7434  df-frecs 8305  df-wrecs 8336  df-recs 8410
This theorem is referenced by:  rdgeq1  8450  rdgeq2  8451  dfoi  9549  oieq1  9550  oieq2  9551  ordtypecbv  9555  dfac12r  10185  zorn2g  10541  ttukey2g  10554  csbrdgg  37312  aomclem3  43045  aomclem8  43050
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