Theorem ax6b 1629

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

Step	Hyp	Ref	Expression
1		ax-ial 1514	. 2 |- ( A. x ph -> A. x A. x ph )
2	1	ax6blem 1628	1 |- ( -. A. x ph -> A. x -. A. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  hbn1  1630  hbnt  1631