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Mirrors > Home > HOLE Home > Th. List > cl | GIF version |
Description: Evaluate a lambda expression. |
Ref | Expression |
---|---|
cl.1 | ⊢ A:β |
cl.2 | ⊢ C:α |
cl.3 | ⊢ [x:α = C]⊧[A = B] |
Ref | Expression |
---|---|
cl | ⊢ ⊤⊧[(λx:α AC) = B] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cl.1 | . 2 ⊢ A:β | |
2 | cl.2 | . 2 ⊢ C:α | |
3 | cl.3 | . 2 ⊢ [x:α = C]⊧[A = B] | |
4 | 1, 3 | eqtypi 69 | . . 3 ⊢ B:β |
5 | wv 58 | . . 3 ⊢ y:α:α | |
6 | 4, 5 | ax-17 95 | . 2 ⊢ ⊤⊧[(λx:α By:α) = B] |
7 | 2, 5 | ax-17 95 | . 2 ⊢ ⊤⊧[(λx:α Cy:α) = C] |
8 | 1, 2, 3, 6, 7 | clf 105 | 1 ⊢ ⊤⊧[(λx:α AC) = B] |
Colors of variables: type var term |
Syntax hints: tv 1 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-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: ovl 107 alval 132 exval 133 euval 134 notval 135 cla4v 142 dfan2 144 cla4ev 159 exmid 186 axpow 208 |
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