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Mirrors > Home > HOLE Home > Th. List > ax17 | GIF version |
Description: Axiom to quantify a variable over a formula in which it does not occur. Axiom C5 in [Megill] p. 444 (p. 11 of the preprint). Also appears as Axiom B6 (p. 75) of system S2 of [Tarski] p. 77 and Axiom C5-1 of [Monk2] p. 113. |
Ref | Expression |
---|---|
ax17.1 | ⊢ A:∗ |
Ref | Expression |
---|---|
ax17 | ⊢ ⊤⊧[A ⇒ (∀λx:α A)] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax17.1 | . 2 ⊢ A:∗ | |
2 | wv 58 | . . 3 ⊢ y:α:α | |
3 | 1, 2 | ax-17 95 | . 2 ⊢ ⊤⊧[(λx:α Ay:α) = A] |
4 | 1, 3 | isfree 176 | 1 ⊢ ⊤⊧[A ⇒ (∀λx:α A)] |
Colors of variables: type var term |
Syntax hints: tv 1 ∗hb 3 kc 5 λkl 6 ⊤kt 8 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 ⇒ tim 111 ∀tal 112 |
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 df-an 118 df-im 119 |
This theorem is referenced by: (None) |
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