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Mirrors > Home > ILE Home > Th. List > ffnd | GIF version |
Description: A mapping is a function with domain, deduction form. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
ffnd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
Ref | Expression |
---|---|
ffnd | ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffnd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5366 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fn wfn 5212 ⟶wf 5213 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 |
This theorem depends on definitions: df-bi 117 df-f 5221 |
This theorem is referenced by: offeq 6096 difinfsn 7099 ctssdc 7112 nnnninfeq 7126 nninfdcinf 7169 nninfwlporlemd 7170 nninfwlporlem 7171 seqvalcd 10459 seq3feq2 10470 seq3feq 10472 seqfeq3 10512 ser0f 10515 facnn 10707 fac0 10708 resunimafz0 10811 seq3shft 10847 fisumss 11400 prodf1f 11551 efcvgfsum 11675 ennnfonelemfun 12418 ennnfonelemf1 12419 mhmf1o 12861 mhmima 12875 mhmeql 12876 grpinvf1o 12940 cnrest2 13739 lmss 13749 lmtopcnp 13753 upxp 13775 uptx 13777 cnmpt11 13786 cnmpt21 13794 cnmpt22f 13798 cnmptcom 13801 hmeof1o2 13811 psmetxrge0 13835 isxmet2d 13851 blelrnps 13922 blelrn 13923 xmetresbl 13943 comet 14002 bdxmet 14004 xmettx 14013 dvidlemap 14163 dvaddxxbr 14168 dvmulxxbr 14169 dvrecap 14180 nninfall 14761 nninfsellemeqinf 14768 nninffeq 14772 refeq 14779 |
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