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Theorem feq23 5258
 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 5256 . 2 (𝐴 = 𝐶 → (𝐹:𝐴𝐵𝐹:𝐶𝐵))
2 feq3 5257 . 2 (𝐵 = 𝐷 → (𝐹:𝐶𝐵𝐹:𝐶𝐷))
31, 2sylan9bb 457 1 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104   = wceq 1331  ⟶wf 5119 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-fn 5126  df-f 5127 This theorem is referenced by:  feq23i  5267
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