Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HOLE Home > Th. List > cbv | GIF version |
Description: Change bound variables in a lambda abstraction. |
Ref | Expression |
---|---|
cbv.1 | ⊢ A:β |
cbv.2 | ⊢ [x:α = y:α]⊧[A = B] |
Ref | Expression |
---|---|
cbv | ⊢ ⊤⊧[λx:α A = λy:α B] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv.1 | . 2 ⊢ A:β | |
2 | wv 58 | . . 3 ⊢ z:α:α | |
3 | 1, 2 | ax-17 95 | . 2 ⊢ ⊤⊧[(λy:α Az:α) = A] |
4 | cbv.2 | . . . 4 ⊢ [x:α = y:α]⊧[A = B] | |
5 | 1, 4 | eqtypi 69 | . . 3 ⊢ B:β |
6 | 5, 2 | ax-17 95 | . 2 ⊢ ⊤⊧[(λx:α Bz:α) = B] |
7 | 1, 3, 6, 4 | cbvf 167 | 1 ⊢ ⊤⊧[λx:α A = λy:α B] |
Colors of variables: type var term |
Syntax hints: tv 1 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-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 |
This theorem is referenced by: ax10 200 |
Copyright terms: Public domain | W3C validator |