ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax6b Unicode version

Theorem ax6b 1584
Description: Quantified Negation. Axiom C5-2 of [Monk2] p. 113.

(Contributed by GD, 27-Jan-2018.)

Assertion
Ref Expression
ax6b  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )

Proof of Theorem ax6b
StepHypRef Expression
1 ax-ial 1470 . 2  |-  ( A. x ph  ->  A. x A. x ph )
21ax6blem 1583 1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1379  ax-gen 1381  ax-ie2 1426  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293
This theorem is referenced by:  hbn1  1585  hbnt  1586
  Copyright terms: Public domain W3C validator