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Axiom ax-7 1752
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 ax7w 1736) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-7

Detailed syntax breakdown of Axiom ax-7
StepHypRef Expression
1 wph . . . 4
2 vy . . . 4
31, 2wal 1550 . . 3
4 vx . . 3
53, 4wal 1550 . 2
61, 4wal 1550 . . 3
76, 2wal 1550 . 2
85, 7wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  a7s  1753  hbal  1754  alcom  1755  hbald  1758  nfaldOLD  1875  cbv1hOLD  1979  hbae  2044  hbaeOLD  2045  sbal1  2210  hbae-o  2237  ax67  2249  ax467  2253  ax11indalem  2281  ax11inda2ALT  2282  hbaltg  25539  pm11.71  27752  ax4567  27757  ax10ext  27762  hbalg  28881  hbalgVD  29258  hbexgVD  29259
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