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Theorem ax6b 1662
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 1545 . 2  |-  ( A. x ph  ->  A. x A. x ph )
21ax6blem 1661 1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ie2 1505  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370
This theorem is referenced by:  hbn1  1663  hbnt  1664
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