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Mirrors > Home > MPE Home > Th. List > caovcan | Structured version Visualization version Unicode version |
Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.) |
Ref | Expression |
---|---|
caovcan.1 | |
caovcan.2 |
Ref | Expression |
---|---|
caovcan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 6657 | . . . 4 | |
2 | oveq1 6657 | . . . 4 | |
3 | 1, 2 | eqeq12d 2637 | . . 3 |
4 | 3 | imbi1d 331 | . 2 |
5 | oveq2 6658 | . . . 4 | |
6 | 5 | eqeq1d 2624 | . . 3 |
7 | eqeq1 2626 | . . 3 | |
8 | 6, 7 | imbi12d 334 | . 2 |
9 | caovcan.1 | . . 3 | |
10 | oveq2 6658 | . . . . . 6 | |
11 | 10 | eqeq2d 2632 | . . . . 5 |
12 | eqeq2 2633 | . . . . 5 | |
13 | 11, 12 | imbi12d 334 | . . . 4 |
14 | 13 | imbi2d 330 | . . 3 |
15 | caovcan.2 | . . 3 | |
16 | 9, 14, 15 | vtocl 3259 | . 2 |
17 | 4, 8, 16 | vtocl2ga 3274 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 (class class class)co 6650 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: ecopovtrn 7850 |
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