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Mirrors > Home > HOLE Home > Th. List > ceq1 | GIF version |
Description: Equality theorem for combination. |
Ref | Expression |
---|---|
ceq12.1 | ⊢ F:(α → β) |
ceq12.2 | ⊢ A:α |
ceq12.3 | ⊢ R⊧[F = T] |
Ref | Expression |
---|---|
ceq1 | ⊢ R⊧[(FA) = (TA)] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceq12.1 | . 2 ⊢ F:(α → β) | |
2 | ceq12.2 | . 2 ⊢ A:α | |
3 | ceq12.3 | . 2 ⊢ R⊧[F = T] | |
4 | 3 | ax-cb1 29 | . . 3 ⊢ R:∗ |
5 | 4, 2 | eqid 73 | . 2 ⊢ R⊧[A = A] |
6 | 1, 2, 3, 5 | ceq12 78 | 1 ⊢ R⊧[(FA) = (TA)] |
Colors of variables: type var term |
Syntax hints: → ht 2 kc 5 = 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: hbxfrf 97 ovl 107 alval 132 exval 133 euval 134 notval 135 ax4g 139 dfan2 144 eta 166 ac 184 ax14 204 axrep 207 axpow 208 axun 209 |
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