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Mirrors > Home > MPE Home > Th. List > ffnd | Structured version Visualization version 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 5958 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fn wfn 5799 ⟶wf 5800 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-f 5808 |
This theorem is referenced by: oprres 6700 isacs4lem 16991 gsumzaddlem 18144 ablfac1eu 18295 lmodfopnelem1 18722 psrbaglefi 19193 psrvscaval 19213 psrlidm 19224 psrridm 19225 psrass1 19226 psrdi 19227 psrdir 19228 mplsubglem 19255 mplvscaval 19269 mplbas2 19291 evlslem3 19335 evlslem1 19336 evlsvar 19344 ptbasfi 21194 rrxmet 22999 itg2cnlem2 23335 mdegldg 23630 fta1glem2 23730 fta1blem 23732 aannenlem1 23887 dchrisum0re 25002 ofpreima2 28849 matunitlindflem1 32575 mblfinlem2 32617 fsovf1od 37330 brcoffn 37348 clsneiel1 37426 ssmapsn 38403 fsumsupp0 38645 volicoff 38888 sge0resrn 39297 sge0le 39300 sge0fodjrnlem 39309 sge0seq 39339 nnfoctbdjlem 39348 meadjiunlem 39358 omeiunle 39407 hoicvr 39438 ovnovollem1 39546 ovnovollem2 39547 iinhoiicclem 39564 iunhoiioolem 39566 preimaicomnf 39599 smfresal 39673 resunimafz0 40368 vtxdgfisf 40691 2pthon3v-av 41150 amgmwlem 42357 |
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