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Theorem feq12i 6688
Description: Equality inference for functions. (Contributed by AV, 7-Feb-2021.)
Hypotheses
Ref Expression
feq12i.1 𝐹 = 𝐺
feq12i.2 𝐴 = 𝐵
Assertion
Ref Expression
feq12i (𝐹:𝐴𝐶𝐺:𝐵𝐶)

Proof of Theorem feq12i
StepHypRef Expression
1 feq12i.1 . 2 𝐹 = 𝐺
2 feq12i.2 . 2 𝐴 = 𝐵
3 eqid 2731 . 2 𝐶 = 𝐶
4 feq123 6685 . 2 ((𝐹 = 𝐺𝐴 = 𝐵𝐶 = 𝐶) → (𝐹:𝐴𝐶𝐺:𝐵𝐶))
51, 2, 3, 4mp3an 1461 1 (𝐹:𝐴𝐶𝐺:𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1541  wf 6519
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3426  df-v 3468  df-dif 3938  df-un 3940  df-in 3942  df-ss 3952  df-nul 4310  df-if 4514  df-sn 4614  df-pr 4616  df-op 4620  df-br 5133  df-opab 5195  df-rel 5667  df-cnv 5668  df-co 5669  df-dm 5670  df-rn 5671  df-fun 6525  df-fn 6526  df-f 6527
This theorem is referenced by:  climlimsupcex  44170
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