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| Mirrors > Home > MPE Home > Th. List > nfa2 | Structured version Visualization version GIF version | ||
| Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2177. (Revised by Wolf Lammen, 18-Oct-2021.) |
| Ref | Expression |
|---|---|
| nfa2 | ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | alcom 2159 | . 2 ⊢ (∀𝑦∀𝑥𝜑 ↔ ∀𝑥∀𝑦𝜑) | |
| 2 | nfa1 2151 | . 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑 | |
| 3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑 |
| Colors of variables: wff setvar class |
| Syntax hints: ∀wal 1538 Ⅎwnf 1783 |
| 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-10 2141 ax-11 2157 |
| This theorem depends on definitions: df-bi 207 df-or 849 df-ex 1780 df-nf 1784 |
| This theorem is referenced by: cbv1h 2410 nfra2w 3299 csbie2t 3937 copsex2t 5497 fnoprabg 7556 bj-hbext 36711 bj-nfext 36713 bj-cbv1hv 36797 ax11-pm 36833 pm14.123b 44445 hbexg 44576 nfich2 47435 ich2al 47454 |
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