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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm10.251 | Structured version Visualization version GIF version |
Description: Theorem *10.251 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.) |
Ref | Expression |
---|---|
pm10.251 | ⊢ (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex 1789 | . 2 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑) | |
2 | 19.2 1985 | . . 3 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑) | |
3 | 2 | con3i 157 | . 2 ⊢ (¬ ∃𝑥𝜑 → ¬ ∀𝑥𝜑) |
4 | 1, 3 | sylbi 220 | 1 ⊢ (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1541 ∃wex 1787 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-6 1976 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: (None) |
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