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Mirrors > Home > ILE Home > Th. List > mpt2eq3dva | Unicode version |
Description: Slightly more general equality inference for the maps to notation. (Contributed by NM, 17-Oct-2013.) |
Ref | Expression |
---|---|
mpt2eq3dva.1 |
Ref | Expression |
---|---|
mpt2eq3dva |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpt2eq3dva.1 | . . . . . 6 | |
2 | 1 | 3expb 1105 | . . . . 5 |
3 | 2 | eqeq2d 2051 | . . . 4 |
4 | 3 | pm5.32da 425 | . . 3 |
5 | 4 | oprabbidv 5559 | . 2 |
6 | df-mpt2 5517 | . 2 | |
7 | df-mpt2 5517 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wcel 1393 coprab 5513 cmpt2 5514 |
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-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-oprab 5516 df-mpt2 5517 |
This theorem is referenced by: mpt2eq3ia 5570 ofeq 5714 fmpt2co 5837 iseqeq2 9215 iseqeq3 9216 iseqval 9220 |
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