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Mirrors > Home > HOLE Home > Th. List > isfree | GIF version |
Description: Derive the metamath "is free" predicate in terms of the HOL "is free" predicate. |
Ref | Expression |
---|---|
alnex1.1 | ⊢ A:∗ |
isfree.2 | ⊢ ⊤⊧[(λx:α Ay:α) = A] |
Ref | Expression |
---|---|
isfree | ⊢ ⊤⊧[A ⇒ (∀λx:α A)] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex1.1 | . . . . 5 ⊢ A:∗ | |
2 | 1 | id 25 | . . . 4 ⊢ A⊧A |
3 | isfree.2 | . . . 4 ⊢ ⊤⊧[(λx:α Ay:α) = A] | |
4 | 2, 3 | alrimi 170 | . . 3 ⊢ A⊧(∀λx:α A) |
5 | 3 | ax-cb1 29 | . . 3 ⊢ ⊤:∗ |
6 | 4, 5 | adantl 51 | . 2 ⊢ (⊤, A)⊧(∀λx:α A) |
7 | 6 | ex 148 | 1 ⊢ ⊤⊧[A ⇒ (∀λx:α A)] |
Colors of variables: type var term |
Syntax hints: tv 1 ∗hb 3 kc 5 λkl 6 = ke 7 ⊤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: ax6 195 ax12 202 ax17 205 |
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