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Mirrors > Home > MPE Home > Th. List > naev2 | Structured version Visualization version GIF version |
Description: Generalization of hbnaev 2068. (Contributed by Wolf Lammen, 9-Apr-2021.) |
Ref | Expression |
---|---|
naev2 | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑡 𝑡 = 𝑢) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | naev 2066 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ¬ ∀𝑣 𝑣 = 𝑤) | |
2 | ax-5 1918 | . 2 ⊢ (¬ ∀𝑣 𝑣 = 𝑤 → ∀𝑧 ¬ ∀𝑣 𝑣 = 𝑤) | |
3 | naev 2066 | . . 3 ⊢ (¬ ∀𝑣 𝑣 = 𝑤 → ¬ ∀𝑡 𝑡 = 𝑢) | |
4 | 3 | alimi 1819 | . 2 ⊢ (∀𝑧 ¬ ∀𝑣 𝑣 = 𝑤 → ∀𝑧 ¬ ∀𝑡 𝑡 = 𝑢) |
5 | 1, 2, 4 | 3syl 18 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑡 𝑡 = 𝑢) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1541 |
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-5 1918 ax-6 1976 ax-7 2016 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 |
This theorem is referenced by: hbnaev 2068 |
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