Axiom ax-5 1557

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.xph -> A.xps))

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 1540	. 2 wff A.x(ph -> ps)
6	1, 4	wal 1540	. . 3 wff A.xph
7	2, 4	wal 1540	. . 3 wff A.xps
8	6, 7	wi 4	. 2 wff (A.xph -> A.xps)
9	5, 8	wi 4	1 wff (A.x(ph -> ps) -> (A.xph -> A.xps))

This axiom is referenced by:  alim  1558  alimi  1559  spfw  1691  spw  1694  ax5o  1749  19.21t  1795  a16g  1945