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Mirrors > Home > ILE Home > Th. List > mpoeq3dva | Unicode version |
Description: Slightly more general equality inference for the maps-to notation. (Contributed by NM, 17-Oct-2013.) |
Ref | Expression |
---|---|
mpoeq3dva.1 |
Ref | Expression |
---|---|
mpoeq3dva |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpoeq3dva.1 | . . . . . 6 | |
2 | 1 | 3expb 1186 | . . . . 5 |
3 | 2 | eqeq2d 2169 | . . . 4 |
4 | 3 | pm5.32da 448 | . . 3 |
5 | 4 | oprabbidv 5878 | . 2 |
6 | df-mpo 5832 | . 2 | |
7 | df-mpo 5832 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wceq 1335 wcel 2128 coprab 5828 cmpo 5829 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-oprab 5831 df-mpo 5832 |
This theorem is referenced by: mpoeq3ia 5889 mpoeq3dv 5890 ofeq 6037 fmpoco 6166 mapxpen 6796 seqeq2 10358 seqeq3 10359 cnmpt2t 12789 cnmpt22 12790 cnmptcom 12794 |
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