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Theorem feq12i 6662
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 2733 . 2 𝐶 = 𝐶
4 feq123 6659 . 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 205   = wceq 1542  wf 6493
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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-fun 6499  df-fn 6500  df-f 6501
This theorem is referenced by:  climlimsupcex  44096
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