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Theorem feq23 5213
 Description: Equality theorem for functions. (Contributed by FL, 14-Jul-2007.) (The proof was shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
feq23 ((A = C B = D) → (F:A–→BF:C–→D))

Proof of Theorem feq23
StepHypRef Expression
1 feq2 5211 . 2 (A = C → (F:A–→BF:C–→B))
2 feq3 5212 . 2 (B = D → (F:C–→BF:C–→D))
31, 2sylan9bb 680 1 ((A = C B = D) → (F:A–→BF:C–→D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642  –→wf 4777 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-fn 4790  df-f 4791 This theorem is referenced by:  feq23i  5219  feq23d  5220
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