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Mirrors > Home > ILE Home > Th. List > fvmpt2 | Unicode version |
Description: Value of a function given by the maps-to notation. (Contributed by FL, 21-Jun-2010.) |
Ref | Expression |
---|---|
fvmpt2.1 |
Ref | Expression |
---|---|
fvmpt2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3052 | . . 3 | |
2 | csbid 3057 | . . 3 | |
3 | 1, 2 | eqtrdi 2219 | . 2 |
4 | fvmpt2.1 | . . 3 | |
5 | nfcv 2312 | . . . 4 | |
6 | nfcsb1v 3082 | . . . 4 | |
7 | csbeq1a 3058 | . . . 4 | |
8 | 5, 6, 7 | cbvmpt 4082 | . . 3 |
9 | 4, 8 | eqtri 2191 | . 2 |
10 | 3, 9 | fvmptg 5570 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 csb 3049 cmpt 4048 cfv 5196 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-mpt 4050 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 |
This theorem is referenced by: fvmptssdm 5578 fvmpt2d 5580 fvmptdf 5581 mpteqb 5584 fvmptt 5585 fvmptf 5586 ralrnmpt 5635 rexrnmpt 5636 fmptco 5659 f1mpt 5747 offval2 6073 ofrfval2 6074 mptelixpg 6708 dom2lem 6746 mapxpen 6822 xpmapenlem 6823 mkvprop 7130 cc2lem 7215 cc3 7217 fsum3cvg 11328 summodclem2a 11331 fsumf1o 11340 fsum3cvg2 11344 fsumadd 11356 isummulc2 11376 fproddccvg 11522 fprodf1o 11538 txcnp 12986 cnmpt11 12998 cnmpt1t 13000 |
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