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Mirrors > Home > ILE Home > Th. List > resmptf | Unicode version |
Description: Restriction of the mapping operation. (Contributed by Thierry Arnoux, 28-Mar-2017.) |
Ref | Expression |
---|---|
resmptf.a | |
resmptf.b |
Ref | Expression |
---|---|
resmptf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resmpt 4862 | . 2 | |
2 | resmptf.a | . . . 4 | |
3 | nfcv 2279 | . . . 4 | |
4 | nfcv 2279 | . . . 4 | |
5 | nfcsb1v 3030 | . . . 4 | |
6 | csbeq1a 3007 | . . . 4 | |
7 | 2, 3, 4, 5, 6 | cbvmptf 4017 | . . 3 |
8 | 7 | reseq1i 4810 | . 2 |
9 | resmptf.b | . . 3 | |
10 | nfcv 2279 | . . 3 | |
11 | 9, 10, 4, 5, 6 | cbvmptf 4017 | . 2 |
12 | 1, 8, 11 | 3eqtr4g 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wnfc 2266 csb 2998 wss 3066 cmpt 3984 cres 4536 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-opab 3985 df-mpt 3986 df-xp 4540 df-rel 4541 df-res 4546 |
This theorem is referenced by: (None) |
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