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Mirrors > Home > MPE Home > Th. List > alex | Structured version Visualization version GIF version |
Description: Theorem 19.6 of [Margaris] p. 89. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
alex | ⊢ (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotb 303 | . . 3 ⊢ (𝜑 ↔ ¬ ¬ 𝜑) | |
2 | 1 | albii 1737 | . 2 ⊢ (∀𝑥𝜑 ↔ ∀𝑥 ¬ ¬ 𝜑) |
3 | alnex 1697 | . 2 ⊢ (∀𝑥 ¬ ¬ 𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑) | |
4 | 2, 3 | bitri 263 | 1 ⊢ (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ∀wal 1473 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: exnal 1744 2nalexn 1745 alimex 1748 19.3v 1884 nfa1 2015 sp 2041 exists2 2550 19.9alt 33270 pm10.253 37583 vk15.4j 37755 vk15.4jVD 38172 |
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