Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HOLE Home > Th. List > hbth | GIF version |
Description: Hypothesis builder for a theorem. |
Ref | Expression |
---|---|
hbth.1 | ⊢ B:α |
hbth.2 | ⊢ R⊧A |
Ref | Expression |
---|---|
hbth | ⊢ R⊧[(λx:α AB) = A] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbth.2 | . . 3 ⊢ R⊧A | |
2 | 1 | ax-cb2 30 | . 2 ⊢ A:∗ |
3 | hbth.1 | . 2 ⊢ B:α | |
4 | wtru 40 | . . 3 ⊢ ⊤:∗ | |
5 | 1 | eqtru 76 | . . 3 ⊢ R⊧[⊤ = A] |
6 | 4, 5 | eqcomi 70 | . 2 ⊢ R⊧[A = ⊤] |
7 | 1 | ax-cb1 29 | . . 3 ⊢ R:∗ |
8 | 4, 3, 7 | a17i 96 | . 2 ⊢ R⊧[(λx:α ⊤B) = ⊤] |
9 | 2, 3, 6, 8 | hbxfr 98 | 1 ⊢ R⊧[(λx:α AB) = A] |
Colors of variables: type var term |
Syntax hints: ∗hb 3 kc 5 λkl 6 = ke 7 ⊤kt 8 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-leq 62 ax-17 95 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: ax4g 139 |
Copyright terms: Public domain | W3C validator |