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Theorem ffnd 5162
Description: A mapping is a function with domain, deduction form. (Contributed by Glauco Siliprandi, 17-Aug-2020.)
Hypothesis
Ref Expression
ffnd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
ffnd (𝜑𝐹 Fn 𝐴)

Proof of Theorem ffnd
StepHypRef Expression
1 ffnd.1 . 2 (𝜑𝐹:𝐴𝐵)
2 ffn 5161 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
31, 2syl 14 1 (𝜑𝐹 Fn 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   Fn wfn 5010  wf 5011
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-f 5019
This theorem is referenced by:  seq3feq2  9893  ser0f  9950  resunimafz0  10236  seq3shft  10272  fisumss  10784  efcvgfsum  10957  nninfalllemn  11898  nninfall  11900  nninfsellemeqinf  11908
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