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Axiom ax-7 1310
Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. One of the predicate logic axioms which do not involve equality. 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  setvar
31, 2wal 1221 . . 3
4 vx . . 3  setvar
53, 4wal 1221 . 2
61, 4wal 1221 . . 3
76, 2wal 1221 . 2
85, 7wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  a7s  1316  alcoms  1338  hbal  1339  alcom  1340  hbald  1353  hbae  1579  bj-hbalt  8168
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