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Mirrors > Home > ILE Home > Th. List > 19.3h | GIF version |
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-May-2007.) |
Ref | Expression |
---|---|
19.3h.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
Ref | Expression |
---|---|
19.3h | ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-4 1497 | . 2 ⊢ (∀𝑥𝜑 → 𝜑) | |
2 | 19.3h.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
3 | 1, 2 | impbii 125 | 1 ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∀wal 1340 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia2 106 ax-ia3 107 ax-4 1497 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 19.27h 1547 19.28h 1549 equsalh 1713 2eu4 2106 |
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