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Theorem feq23 6261
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 6259 . 2 (𝐴 = 𝐶 → (𝐹:𝐴𝐵𝐹:𝐶𝐵))
2 feq3 6260 . 2 (𝐵 = 𝐷 → (𝐹:𝐶𝐵𝐹:𝐶𝐷))
31, 2sylan9bb 507 1 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wa 386   = wceq 1658  wf 6118
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2802
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2811  df-cleq 2817  df-clel 2820  df-in 3804  df-ss 3811  df-fn 6125  df-f 6126
This theorem is referenced by:  feq23i  6271  ismgmOLD  34190  ismndo2  34214  rngomndo  34275  seff  39347
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