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Theorem funfni 5574
 Description: Inference to convert a function and domain antecedent. (Contributed by NM, 22-Apr-2004.)
Hypothesis
Ref Expression
funfni.1
Assertion
Ref Expression
funfni

Proof of Theorem funfni
StepHypRef Expression
1 fnfun 5571 . . 3
3 fndm 5573 . . . 4
43eleq2d 2509 . . 3
54biimpar 473 . 2
6 funfni.1 . 2
72, 5, 6syl2anc 644 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1727   cdm 4907   wfun 5477   wfn 5478 This theorem is referenced by:  fneu  5578  elpreima  5879  fnopfv  5894  fnfvelrn  5896  funressnfv  28006  fnafvelrn  28047  afvco2  28054 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-11 1763  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2435  df-clel 2438  df-fn 5486
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