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Axiom ax-7 1273
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 (xyφyxφ)

Detailed syntax breakdown of Axiom ax-7
StepHypRef Expression
1 wph . . . 4 wff φ
2 vy . . . 4 set y
31, 2wal 1271 . . 3 wff yφ
4 vx . . 3 set x
53, 4wal 1271 . 2 wff xyφ
61, 4wal 1271 . . 3 wff xφ
76, 2wal 1271 . 2 wff yxφ
85, 7wi 4 1 wff (xyφyxφ)
Colors of variables: wff set class
This axiom is referenced by:  a7s  1279  hbal  1301  alcom  1302  hbald  1317  hbae  1524
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