Axiom ax-6 1729

Description: Axiom of Quantified Negation. Axiom C5-2 of [Monk2] p. 113. This axiom scheme is logically redundant (see ax6w 1717) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
ax-6	|- (-. A.xph -> A.x -. A.xph)

Detailed syntax breakdown of Axiom ax-6

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff ph
2		vx	. . . 4 setvar x
3	1, 2	wal 1540	. . 3 wff A.xph
4	3	wn 3	. 2 wff -. A.xph
5	4, 2	wal 1540	. 2 wff A.x -. A.xph
6	4, 5	wi 4	1 wff (-. A.xph -> A.x -. A.xph)

This axiom is referenced by:  hbn1  1730  ax6o  1750