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Mirrors > Home > MPE Home > Th. List > nexdvOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nexdv 1851 as of 10-Oct-2021. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 13-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nexdv.1 | ⊢ (𝜑 → ¬ 𝜓) |
Ref | Expression |
---|---|
nexdvOLD | ⊢ (𝜑 → ¬ ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexdv.1 | . . 3 ⊢ (𝜑 → ¬ 𝜓) | |
2 | 1 | alrimiv 1842 | . 2 ⊢ (𝜑 → ∀𝑥 ¬ 𝜓) |
3 | alnex 1697 | . 2 ⊢ (∀𝑥 ¬ 𝜓 ↔ ¬ ∃𝑥𝜓) | |
4 | 2, 3 | sylib 207 | 1 ⊢ (𝜑 → ¬ ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀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 ax-5 1827 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: (None) |
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