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Mirrors > Home > ILE Home > Th. List > ofeq | Unicode version |
Description: Equality theorem for function operation. (Contributed by Mario Carneiro, 20-Jul-2014.) |
Ref | Expression |
---|---|
ofeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 904 | . . . . 5 | |
2 | 1 | oveqd 5529 | . . . 4 |
3 | 2 | mpteq2dv 3848 | . . 3 |
4 | 3 | mpt2eq3dva 5569 | . 2 |
5 | df-of 5712 | . 2 | |
6 | df-of 5712 | . 2 | |
7 | 4, 5, 6 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 885 wceq 1243 wcel 1393 cvv 2557 cin 2916 cmpt 3818 cdm 4345 cfv 4902 (class class class)co 5512 cmpt2 5514 cof 5710 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-iota 4867 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 df-of 5712 |
This theorem is referenced by: (None) |
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