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Axiom ax-7 1338
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. An alternate axiomatization could use ax467 1455 in place of ax-4 1392, ax-6o 1428, and ax-7 1338.
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 1335 . . 3 wff yφ
4 vx . . 3 set x
53, 4wal 1335 . 2 wff xyφ
61, 4wal 1335 . . 3 wff xφ
76, 2wal 1335 . 2 wff yxφ
85, 7wi 4 1 wff (xyφyxφ)
Colors of variables: wff set class
This axiom is referenced by:  a7s  1344  hbal  1357  alcom  1358  hbald  1373  ax67  1452  ax467  1455  hbae  1578  cbv1  1595  sbal1  1793  ax11indalem  1815  ax11inda2ALT  1816
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