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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 2171. (Revised by Wolf Lammen, 18-Oct-2021.) |
Ref | Expression |
---|---|
nfa2 | ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 2156 | . 2 ⊢ (∀𝑦∀𝑥𝜑 ↔ ∀𝑥∀𝑦𝜑) | |
2 | nfa1 2148 | . 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑 | |
3 | 1, 2 | nfxfr 1855 | 1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1537 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-10 2137 ax-11 2154 |
This theorem depends on definitions: df-bi 206 df-or 845 df-ex 1783 df-nf 1787 |
This theorem is referenced by: cbv1h 2405 csbie2t 3872 copsex2t 5404 fnoprabg 7387 bj-hbext 34900 bj-nfext 34902 bj-cbv1hv 34986 ax11-pm 35023 pm14.123b 42025 hbexg 42157 nfich2 44878 ich2al 44897 |
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