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Mirrors > Home > ILE Home > Th. List > caovcang | Unicode version |
Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovcang.1 |
Ref | Expression |
---|---|
caovcang |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovcang.1 | . . 3 | |
2 | 1 | ralrimivvva 2540 | . 2 |
3 | oveq1 5833 | . . . . 5 | |
4 | oveq1 5833 | . . . . 5 | |
5 | 3, 4 | eqeq12d 2172 | . . . 4 |
6 | 5 | bibi1d 232 | . . 3 |
7 | oveq2 5834 | . . . . 5 | |
8 | 7 | eqeq1d 2166 | . . . 4 |
9 | eqeq1 2164 | . . . 4 | |
10 | 8, 9 | bibi12d 234 | . . 3 |
11 | oveq2 5834 | . . . . 5 | |
12 | 11 | eqeq2d 2169 | . . . 4 |
13 | eqeq2 2167 | . . . 4 | |
14 | 12, 13 | bibi12d 234 | . . 3 |
15 | 6, 10, 14 | rspc3v 2832 | . 2 |
16 | 2, 15 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 963 wceq 1335 wcel 2128 wral 2435 (class class class)co 5826 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-iota 5137 df-fv 5180 df-ov 5829 |
This theorem is referenced by: caovcand 5985 |
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