Axiom ax-4 1737

Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105 and Theorem 19.20 of [Margaris] p. 90. It is restated as alim 1738 for labeling consistency. It should be used only by alim 1738. (Contributed by NM, 21-May-2008.) Use alim 1738 instead. (New usage is discouraged.)

Assertion

Ref	Expression
ax-4	|- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )

Detailed syntax breakdown of Axiom ax-4

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 1481	. 2 wff A. x ( ph -> ps )
6	1, 4	wal 1481	. . 3 wff A. x ph
7	2, 4	wal 1481	. . 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:  alim  1738