| Mathbox for Wolf Lammen |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-ax11-lem7 | Structured version Visualization version GIF version | ||
| Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.) |
| Ref | Expression |
|---|---|
| wl-ax11-lem7 | ⊢ (∀𝑥(¬ ∀𝑥 𝑥 = 𝑦 ∧ 𝜑) ↔ (¬ ∀𝑥 𝑥 = 𝑦 ∧ ∀𝑥𝜑)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfna1 2152 | . 2 ⊢ Ⅎ𝑥 ¬ ∀𝑥 𝑥 = 𝑦 | |
| 2 | 1 | 19.28 2228 | 1 ⊢ (∀𝑥(¬ ∀𝑥 𝑥 = 𝑦 ∧ 𝜑) ↔ (¬ ∀𝑥 𝑥 = 𝑦 ∧ ∀𝑥𝜑)) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 ↔ wb 206 ∧ wa 395 ∀wal 1538 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 |
| This theorem is referenced by: wl-ax11-lem8 37593 |
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