Axiom ax-5 1435

Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
ax-5	|- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )

Detailed syntax breakdown of Axiom ax-5

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff ph
2		wps	. . . 4 wff ps
3	1, 2	wi 4	. . 3 wff ( ph -> ps )
4		vx	. . 3 setvar x
5	3, 4	wal 1341	. 2 wff A. x ( ph -> ps )
6	1, 4	wal 1341	. . 3 wff A. x ph
7	2, 4	wal 1341	. . 3 wff A. x ps
8	6, 7	wi 4	. 2 wff ( A. x ph -> A. x ps )
9	5, 8	wi 4	1 wff ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )

This axiom is referenced by:  alimi  1443  alim  1445  nfrimi  1513  a5i  1531  nfal  1564