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Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c7toc5 | Structured version Visualization version GIF version |
Description: Rederivation of ax-c5 33186 from axc5c7 33214. Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axc5c7toc5 | ⊢ (∀𝑥𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (∀𝑥𝜑 → (∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑)) | |
2 | axc5c7 33214 | . 2 ⊢ ((∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∀𝑥𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-c5 33186 ax-c7 33188 |
This theorem is referenced by: (None) |
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