![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 19.9h | GIF version |
Description: A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of [Margaris] p. 89. (Contributed by FL, 24-Mar-2007.) |
Ref | Expression |
---|---|
19.9h.1 | ⊢ (φ → ∀xφ) |
Ref | Expression |
---|---|
19.9h | ⊢ (∃xφ ↔ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.9ht 1529 | . . 3 ⊢ (∀x(φ → ∀xφ) → (∃xφ → φ)) | |
2 | 19.9h.1 | . . 3 ⊢ (φ → ∀xφ) | |
3 | 1, 2 | mpg 1337 | . 2 ⊢ (∃xφ → φ) |
4 | 19.8a 1479 | . 2 ⊢ (φ → ∃xφ) | |
5 | 3, 4 | impbii 117 | 1 ⊢ (∃xφ ↔ φ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∀wal 1240 ∃wex 1378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: 19.9 1532 excomim 1550 exdistrfor 1678 sbcof2 1688 ax11ev 1706 19.9v 1748 exists1 1993 |
Copyright terms: Public domain | W3C validator |