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Theorem feq23 6692
Description: Equality theorem for functions. (Contributed by FL, 14-Jul-2007.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
feq23 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))

Proof of Theorem feq23
StepHypRef Expression
1 feq2 6690 . 2 (𝐴 = 𝐶 → (𝐹:𝐴𝐵𝐹:𝐶𝐵))
2 feq3 6691 . 2 (𝐵 = 𝐷 → (𝐹:𝐶𝐵𝐹:𝐶𝐷))
31, 2sylan9bb 509 1 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 395   = wceq 1533  wf 6530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-in 3948  df-ss 3958  df-fn 6537  df-f 6538
This theorem is referenced by:  feq23i  6702  ismgmOLD  37221  ismndo2  37245  rngomndo  37306  seff  43617
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