Axiom ax-11 1748

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 1732) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
ax-11

Detailed syntax breakdown of Axiom ax-11

Step	Hyp	Ref	Expression
1		wph	. . . 4
2		vy	. . . 4
3	1, 2	wal 1556	. . 3
4		vx	. . 3
5	3, 4	wal 1556	. 2
6	1, 4	wal 1556	. . 3
7	6, 2	wal 1556	. 2
8	5, 7	wi 4	1

This axiom is referenced by:  alcoms  1749  hbal  1750  alcom  1751  hbald  1754  nfaldOLD  1867  cbv1hOLD  1974  hbae  2037  hbaeOLD  2038  sbal1OLD  2224  hbae-o  2255  axc711  2267  axc5c711  2271  ax12indalem  2298  ax12inda2ALT  2299  hbaltg  26265  pm11.71  28499  axc5c4c711  28504  axc11next  28509  hbalg  29833  hbalgVD  30210  hbexgVD  30211