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Theorem f1eq2 5254
 Description: Equality theorem for one-to-one functions. (Contributed by set.mm contributors, 10-Feb-1997.)
Assertion
Ref Expression
f1eq2 (A = B → (F:A1-1CF:B1-1C))

Proof of Theorem f1eq2
StepHypRef Expression
1 feq2 5211 . . 3 (A = B → (F:A–→CF:B–→C))
21anbi1d 685 . 2 (A = B → ((F:A–→C Fun F) ↔ (F:B–→C Fun F)))
3 df-f1 4792 . 2 (F:A1-1C ↔ (F:A–→C Fun F))
4 df-f1 4792 . 2 (F:B1-1C ↔ (F:B–→C Fun F))
52, 3, 43bitr4g 279 1 (A = B → (F:A1-1CF:B1-1C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642  ◡ccnv 4771  Fun wfun 4775  –→wf 4777  –1-1→wf1 4778 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-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4790  df-f 4791  df-f1 4792 This theorem is referenced by:  f1oeq2  5282  dflec3  6221  nclenc  6222
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