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Axiom ax-7 1217
Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. One of the 4 axioms of pure predicate calculus. 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. (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 1214 . . 3
4 vx . . 3
53, 4wal 1214 . 2
61, 4wal 1214 . . 3
76, 2wal 1214 . 2
85, 7wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  a7s  1223  hbal  1236  alcom  1237  hbald  1252  hbae  1408  cbv1  1427  sbal1  1644  ax11indalem  1814  ax11inda2ALT  1815
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