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Mirrors > Home > ILE Home > Th. List > mpt2eq123dva | Unicode version |
Description: An equality deduction for the maps to notation. (Contributed by Mario Carneiro, 26-Jan-2017.) |
Ref | Expression |
---|---|
mpt2eq123dv.1 | |
mpt2eq123dva.2 | |
mpt2eq123dva.3 |
Ref | Expression |
---|---|
mpt2eq123dva |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpt2eq123dva.3 | . . . . . 6 | |
2 | 1 | eqeq2d 2092 | . . . . 5 |
3 | 2 | pm5.32da 439 | . . . 4 |
4 | mpt2eq123dva.2 | . . . . . . . 8 | |
5 | 4 | eleq2d 2148 | . . . . . . 7 |
6 | 5 | pm5.32da 439 | . . . . . 6 |
7 | mpt2eq123dv.1 | . . . . . . . 8 | |
8 | 7 | eleq2d 2148 | . . . . . . 7 |
9 | 8 | anbi1d 452 | . . . . . 6 |
10 | 6, 9 | bitrd 186 | . . . . 5 |
11 | 10 | anbi1d 452 | . . . 4 |
12 | 3, 11 | bitrd 186 | . . 3 |
13 | 12 | oprabbidv 5579 | . 2 |
14 | df-mpt2 5537 | . 2 | |
15 | df-mpt2 5537 | . 2 | |
16 | 13, 14, 15 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 coprab 5533 cmpt2 5534 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-oprab 5536 df-mpt2 5537 |
This theorem is referenced by: mpt2eq123dv 5587 |
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