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Theorem feq12i 6593
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 2738 . 2 𝐶 = 𝐶
4 feq123 6590 . 2 ((𝐹 = 𝐺𝐴 = 𝐵𝐶 = 𝐶) → (𝐹:𝐴𝐶𝐺:𝐵𝐶))
51, 2, 3, 4mp3an 1460 1 (𝐹:𝐴𝐶𝐺:𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1539  wf 6429
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-br 5075  df-opab 5137  df-rel 5596  df-cnv 5597  df-co 5598  df-dm 5599  df-rn 5600  df-fun 6435  df-fn 6436  df-f 6437
This theorem is referenced by:  climlimsupcex  43310
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