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Mirrors > Home > MPE Home > Th. List > ax-11 | Unicode version |
Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. Axiom scheme C6' in [Megill] p. 448 (p. 16 of the preprint). Also appears as Lemma 12 of [Monk2] p. 109 and Axiom C5-3 of [Monk2] p. 113. This axiom scheme is logically redundant (see ax11w 1826) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
ax-11 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . 4 | |
2 | vy | . . . 4 | |
3 | 1, 2 | wal 1393 | . . 3 |
4 | vx | . . 3 | |
5 | 3, 4 | wal 1393 | . 2 |
6 | 1, 4 | wal 1393 | . . 3 |
7 | 6, 2 | wal 1393 | . 2 |
8 | 5, 7 | wi 4 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: alcoms 1843 hbal 1844 alcom 1845 hbald 1848 hbae 2055 hbae-o 2232 axc711 2244 axc5c711 2248 ax12indalem 2275 ax12inda2ALT 2276 hbaltg 29240 pm11.71 31303 axc5c4c711 31308 axc11next 31313 hbalg 33328 hbalgVD 33705 hbexgVD 33706 bj-hbalt 34240 |
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