ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-7 GIF version

Axiom ax-7 1256
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 (xyφyxφ)

Detailed syntax breakdown of Axiom ax-7
StepHypRef Expression
1 wph . . . 4 wff φ
2 vy . . . 4 set y
31, 2wal 1253 . . 3 wff yφ
4 vx . . 3 set x
53, 4wal 1253 . 2 wff xyφ
61, 4wal 1253 . . 3 wff xφ
76, 2wal 1253 . 2 wff yxφ
85, 7wi 4 1 wff (xyφyxφ)
Colors of variables: wff set class
This axiom is referenced by:  a7s  1262  hbal  1275  alcom  1276  hbald  1291  hbae  1457  cbv1  1474  sbal1  1672  ax11indalem  1790  ax11inda2ALT  1791
  Copyright terms: Public domain W3C validator