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Theorem feq23 5134
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 5132 . 2 (𝐴 = 𝐶 → (𝐹:𝐴𝐵𝐹:𝐶𝐵))
2 feq3 5133 . 2 (𝐵 = 𝐷 → (𝐹:𝐶𝐵𝐹:𝐶𝐷))
31, 2sylan9bb 450 1 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103   = wceq 1289  wf 4998
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010  df-fn 5005  df-f 5006
This theorem is referenced by:  feq23i  5142
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