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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 2402 | . 2 |
3 | oveq1 5519 | . . . . 5 | |
4 | oveq1 5519 | . . . . 5 | |
5 | 3, 4 | eqeq12d 2054 | . . . 4 |
6 | 5 | bibi1d 222 | . . 3 |
7 | oveq2 5520 | . . . . 5 | |
8 | 7 | eqeq1d 2048 | . . . 4 |
9 | eqeq1 2046 | . . . 4 | |
10 | 8, 9 | bibi12d 224 | . . 3 |
11 | oveq2 5520 | . . . . 5 | |
12 | 11 | eqeq2d 2051 | . . . 4 |
13 | eqeq2 2049 | . . . 4 | |
14 | 12, 13 | bibi12d 224 | . . 3 |
15 | 6, 10, 14 | rspc3v 2665 | . 2 |
16 | 2, 15 | mpan9 265 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wral 2306 (class class class)co 5512 |
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-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 |
This theorem is referenced by: caovcand 5663 |
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