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Mirrors > Home > NFE Home > Th. List > mpt2eq123dv | Unicode version |
Description: An equality deduction for the maps to notation. (Contributed by set.mm contributors, 12-Sep-2011.) |
Ref | Expression |
---|---|
mpt2eq123dv.1 | |
mpt2eq123dv.2 | |
mpt2eq123dv.3 |
Ref | Expression |
---|---|
mpt2eq123dv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpt2eq123dv.1 | . . . . . 6 | |
2 | 1 | eleq2d 2420 | . . . . 5 |
3 | mpt2eq123dv.2 | . . . . . 6 | |
4 | 3 | eleq2d 2420 | . . . . 5 |
5 | 2, 4 | anbi12d 691 | . . . 4 |
6 | mpt2eq123dv.3 | . . . . 5 | |
7 | 6 | eqeq2d 2364 | . . . 4 |
8 | 5, 7 | anbi12d 691 | . . 3 |
9 | 8 | oprabbidv 5564 | . 2 |
10 | df-mpt2 5654 | . 2 | |
11 | df-mpt2 5654 | . 2 | |
12 | 9, 10, 11 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 wcel 1710 coprab 5527 cmpt2 5653 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-oprab 5528 df-mpt2 5654 |
This theorem is referenced by: mpt2eq123i 5664 |
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