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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
StepHypRef Expression
1 wph . . . 4
2 vy . . . 4
31, 2wal 1564 . . 3
4 vx . . 3
53, 4wal 1564 . 2
61, 4wal 1564 . . 3
76, 2wal 1564 . 2
85, 7wi 4 1
Colors of variables: wff set class
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
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