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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 5365 | . 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 5211 ⟶wf 5212 |
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 5220 |
This theorem is referenced by: offeq 6095 difinfsn 7098 ctssdc 7111 nnnninfeq 7125 nninfdcinf 7168 nninfwlporlemd 7169 nninfwlporlem 7170 seqvalcd 10458 seq3feq2 10469 seq3feq 10471 seqfeq3 10511 ser0f 10514 facnn 10706 fac0 10707 resunimafz0 10810 seq3shft 10846 fisumss 11399 prodf1f 11550 efcvgfsum 11674 ennnfonelemfun 12417 ennnfonelemf1 12418 mhmf1o 12860 mhmima 12874 mhmeql 12875 grpinvf1o 12939 cnrest2 13706 lmss 13716 lmtopcnp 13720 upxp 13742 uptx 13744 cnmpt11 13753 cnmpt21 13761 cnmpt22f 13765 cnmptcom 13768 hmeof1o2 13778 psmetxrge0 13802 isxmet2d 13818 blelrnps 13889 blelrn 13890 xmetresbl 13910 comet 13969 bdxmet 13971 xmettx 13980 dvidlemap 14130 dvaddxxbr 14135 dvmulxxbr 14136 dvrecap 14147 nninfall 14728 nninfsellemeqinf 14735 nninffeq 14739 refeq 14746 |
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