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Theorem feq12i 6728
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 2736 . 2 𝐶 = 𝐶
4 feq123 6725 . 2 ((𝐹 = 𝐺𝐴 = 𝐵𝐶 = 𝐶) → (𝐹:𝐴𝐶𝐺:𝐵𝐶))
51, 2, 3, 4mp3an 1462 1 (𝐹:𝐴𝐶𝐺:𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1539  wf 6556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-br 5143  df-opab 5205  df-rel 5691  df-cnv 5692  df-co 5693  df-dm 5694  df-rn 5695  df-fun 6562  df-fn 6563  df-f 6564
This theorem is referenced by:  climlimsupcex  45789
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