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Mirrors > Home > HOLE Home > Th. List > oveq12 | GIF version |
Description: Equality theorem for binary operation. |
Ref | Expression |
---|---|
oveq.1 | ⊢ F:(α → (β → γ)) |
oveq.2 | ⊢ A:α |
oveq.3 | ⊢ B:β |
oveq1.4 | ⊢ R⊧[A = C] |
oveq12.5 | ⊢ R⊧[B = T] |
Ref | Expression |
---|---|
oveq12 | ⊢ R⊧[[AFB] = [CFT]] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq.1 | . 2 ⊢ F:(α → (β → γ)) | |
2 | oveq.2 | . 2 ⊢ A:α | |
3 | oveq.3 | . 2 ⊢ B:β | |
4 | oveq1.4 | . . . 4 ⊢ R⊧[A = C] | |
5 | 4 | ax-cb1 29 | . . 3 ⊢ R:∗ |
6 | 5, 1 | eqid 73 | . 2 ⊢ R⊧[F = F] |
7 | oveq12.5 | . 2 ⊢ R⊧[B = T] | |
8 | 1, 2, 3, 6, 4, 7 | oveq123 88 | 1 ⊢ R⊧[[AFB] = [CFT]] |
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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