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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 4084 | . . 3 |
9 | 4, 8 | eqtri 2191 | . 2 |
10 | 3, 9 | fvmptg 5572 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 csb 3049 cmpt 4050 cfv 5198 |
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 4107 ax-pow 4160 ax-pr 4194 |
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 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 |
This theorem is referenced by: fvmptssdm 5580 fvmpt2d 5582 fvmptdf 5583 mpteqb 5586 fvmptt 5587 fvmptf 5588 fnmptfvd 5600 ralrnmpt 5638 rexrnmpt 5639 fmptco 5662 f1mpt 5750 offval2 6076 ofrfval2 6077 mptelixpg 6712 dom2lem 6750 mapxpen 6826 xpmapenlem 6827 mkvprop 7134 cc2lem 7228 cc3 7230 fsum3cvg 11341 summodclem2a 11344 fsumf1o 11353 fsum3cvg2 11357 fsumadd 11369 isummulc2 11389 fproddccvg 11535 fprodf1o 11551 txcnp 13065 cnmpt11 13077 cnmpt1t 13079 |
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