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Mirrors > Home > ILE Home > Th. List > mpteq12f | Unicode version |
Description: An equality theorem for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq12f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1434 | . . . 4 | |
2 | nfra1 2355 | . . . 4 | |
3 | 1, 2 | nfan 1457 | . . 3 |
4 | nfv 1421 | . . 3 | |
5 | rsp 2369 | . . . . . . 7 | |
6 | 5 | imp 115 | . . . . . 6 |
7 | 6 | eqeq2d 2051 | . . . . 5 |
8 | 7 | pm5.32da 425 | . . . 4 |
9 | sp 1401 | . . . . . 6 | |
10 | 9 | eleq2d 2107 | . . . . 5 |
11 | 10 | anbi1d 438 | . . . 4 |
12 | 8, 11 | sylan9bbr 436 | . . 3 |
13 | 3, 4, 12 | opabbid 3822 | . 2 |
14 | df-mpt 3820 | . 2 | |
15 | df-mpt 3820 | . 2 | |
16 | 13, 14, 15 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wceq 1243 wcel 1393 wral 2306 copab 3817 cmpt 3818 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-opab 3819 df-mpt 3820 |
This theorem is referenced by: mpteq12dva 3838 mpteq12 3840 mpteq2ia 3843 mpteq2da 3846 |
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