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Theorem feq12i 5933
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 2605 . 2 𝐶 = 𝐶
4 feq123 5930 . 2 ((𝐹 = 𝐺𝐴 = 𝐵𝐶 = 𝐶) → (𝐹:𝐴𝐶𝐺:𝐵𝐶))
51, 2, 3, 4mp3an 1415 1 (𝐹:𝐴𝐶𝐺:𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wb 194   = wceq 1474  wf 5782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2228  ax-ext 2585
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-nfc 2735  df-rab 2900  df-v 3170  df-dif 3538  df-un 3540  df-in 3542  df-ss 3549  df-nul 3870  df-if 4032  df-sn 4121  df-pr 4123  df-op 4127  df-br 4574  df-opab 4634  df-rel 5031  df-cnv 5032  df-co 5033  df-dm 5034  df-rn 5035  df-fun 5788  df-fn 5789  df-f 5790
This theorem is referenced by: (None)
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