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Mirrors > Home > HOLE Home > Th. List > dfov2 | GIF version |
Description: Reverse direction of df-ov 65. |
Ref | Expression |
---|---|
dfov1.1 | ⊢ F:(α → (β → ∗)) |
dfov1.2 | ⊢ A:α |
dfov1.3 | ⊢ B:β |
dfov2.4 | ⊢ R⊧((FA)B) |
Ref | Expression |
---|---|
dfov2 | ⊢ R⊧[AFB] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfov1.1 | . . 3 ⊢ F:(α → (β → ∗)) | |
2 | dfov1.2 | . . 3 ⊢ A:α | |
3 | dfov1.3 | . . 3 ⊢ B:β | |
4 | 1, 2, 3 | wov 64 | . 2 ⊢ [AFB]:∗ |
5 | dfov2.4 | . 2 ⊢ R⊧((FA)B) | |
6 | 5 | ax-cb1 29 | . . 3 ⊢ R:∗ |
7 | 1, 2, 3 | df-ov 65 | . . 3 ⊢ ⊤⊧(( = [AFB])((FA)B)) |
8 | 6, 7 | a1i 28 | . 2 ⊢ R⊧(( = [AFB])((FA)B)) |
9 | 4, 5, 8 | mpbirx 48 | 1 ⊢ R⊧[AFB] |
Colors of variables: type var term |
Syntax hints: → ht 2 ∗hb 3 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: eqcomi 70 eqid 73 ded 74 ceq12 78 leq 81 beta 82 distrc 83 distrl 84 eqtri 85 oveq123 88 hbov 101 ovl 107 |
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