Axiom ax-11 1756

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 1740) 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 1564	. . 3
4		vx	. . 3
5	3, 4	wal 1564	. 2
6	1, 4	wal 1564	. . 3
7	6, 2	wal 1564	. 2
8	5, 7	wi 4	1

This axiom is referenced by:  alcoms  1757  hbal  1758  alcom  1759  hbald  1762  nfaldOLD  1875  cbv1hOLD  1982  hbae  2045  hbaeOLD  2046  sbal1OLD  2232  hbae-o  2263  axc711  2275  axc5c711  2279  ax12indalem  2306  ax12inda2ALT  2307  hbaltg  26774  pm11.71  28824  axc5c4c711  28829  axc11next  28834  hbalg  30110  hbalgVD  30487  hbexgVD  30488