MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-11 Unicode version

Axiom ax-11 1842
Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. 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. This axiom scheme is logically redundant (see ax11w 1826) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
ax-11

Detailed syntax breakdown of Axiom ax-11
StepHypRef Expression
1 wph . . . 4
2 vy . . . 4
31, 2wal 1393 . . 3
4 vx . . 3
53, 4wal 1393 . 2
61, 4wal 1393 . . 3
76, 2wal 1393 . 2
85, 7wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  alcoms  1843  hbal  1844  alcom  1845  hbald  1848  hbae  2055  hbae-o  2232  axc711  2244  axc5c711  2248  ax12indalem  2275  ax12inda2ALT  2276  hbaltg  29240  pm11.71  31303  axc5c4c711  31308  axc11next  31313  hbalg  33328  hbalgVD  33705  hbexgVD  33706  bj-hbalt  34240
  Copyright terms: Public domain W3C validator