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

Axiom ax-7 1313
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 1224 . . 3
4 vx . . 3  setvar
53, 4wal 1224 . 2
61, 4wal 1224 . . 3
76, 2wal 1224 . 2
85, 7wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  a7s  1319  alcoms  1341  hbal  1342  alcom  1343  hbald  1357  hbae  1584  bj-hbalt  7202
  Copyright terms: Public domain W3C validator