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Mirrors > Home > ILE Home > Th. List > mpteq1 | Unicode version |
Description: An equality theorem for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2041 | . . 3 | |
2 | 1 | rgen 2374 | . 2 |
3 | mpteq12 3840 | . 2 | |
4 | 2, 3 | mpan2 401 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 wral 2306 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: mpteq1d 3842 fmptap 5353 mpt2mpt 5596 mpt2mptsx 5823 mpt2mpts 5824 tposf12 5884 |
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