Axiom ax-11 1842

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.)

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 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

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