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Mirrors > Home > HOLE Home > Th. List > oveq12 | Unicode version |
Description: Equality theorem for binary operation. |
Ref | Expression |
---|---|
oveq.1 | |
oveq.2 | |
oveq.3 | |
oveq1.4 | |
oveq12.5 |
Ref | Expression |
---|---|
oveq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq.1 | . 2 | |
2 | oveq.2 | . 2 | |
3 | oveq.3 | . 2 | |
4 | oveq1.4 | . . . 4 | |
5 | 4 | ax-cb1 29 | . . 3 |
6 | 5, 1 | eqid 73 | . 2 |
7 | oveq12.5 | . 2 | |
8 | 1, 2, 3, 6, 4, 7 | oveq123 88 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 ke 7 kbr 9 wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: oveq2 91 clf 105 imval 136 dfan2 144 ecase 153 exlimdv2 156 eta 166 cbvf 167 leqf 169 exlimd 171 ac 184 |
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