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Mirrors > Home > ILE Home > Th. List > caovcomg | Unicode version |
Description: Convert an operation commutative law to class notation. (Contributed by Mario Carneiro, 1-Jun-2013.) |
Ref | Expression |
---|---|
caovcomg.1 |
Ref | Expression |
---|---|
caovcomg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovcomg.1 | . . 3 | |
2 | 1 | ralrimivva 2552 | . 2 |
3 | oveq1 5858 | . . . 4 | |
4 | oveq2 5859 | . . . 4 | |
5 | 3, 4 | eqeq12d 2185 | . . 3 |
6 | oveq2 5859 | . . . 4 | |
7 | oveq1 5858 | . . . 4 | |
8 | 6, 7 | eqeq12d 2185 | . . 3 |
9 | 5, 8 | rspc2v 2847 | . 2 |
10 | 2, 9 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 wral 2448 (class class class)co 5851 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5854 |
This theorem is referenced by: caovcomd 6007 caovcom 6008 caovlem2d 6043 caofcom 6082 seq3caopr 10428 |
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