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Mirrors > Home > HOLE Home > Th. List > 19.8a | GIF version |
Description: Existential introduction. |
Ref | Expression |
---|---|
19.8a.1 | ⊢ A:∗ |
Ref | Expression |
---|---|
19.8a | ⊢ A⊧(∃λx:α A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a.1 | . . . 4 ⊢ A:∗ | |
2 | 1 | ax-id 24 | . . 3 ⊢ A⊧A |
3 | 1 | beta 82 | . . . 4 ⊢ ⊤⊧[(λx:α Ax:α) = A] |
4 | 1, 3 | a1i 28 | . . 3 ⊢ A⊧[(λx:α Ax:α) = A] |
5 | 2, 4 | mpbir 77 | . 2 ⊢ A⊧(λx:α Ax:α) |
6 | 1 | wl 59 | . . 3 ⊢ λx:α A:(α → ∗) |
7 | wv 58 | . . 3 ⊢ x:α:α | |
8 | 6, 7 | ax4e 158 | . 2 ⊢ (λx:α Ax:α)⊧(∃λx:α A) |
9 | 5, 8 | syl 16 | 1 ⊢ A⊧(∃λx:α A) |
Colors of variables: type var term |
Syntax hints: tv 1 ∗hb 3 kc 5 λkl 6 = ke 7 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 ∃tex 113 |
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 |
This theorem depends on definitions: df-ov 65 df-al 116 df-an 118 df-im 119 df-ex 121 |
This theorem is referenced by: eximdv 173 alnex 174 ax9 199 |
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