Axiom ax-5 1140

Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105.

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 3	. . 3 wff (ph -> ps)
4		vx	. . 3 set x
5	3, 4	wal 1134	. 2 wff A.x(ph -> ps)
6	1, 4	wal 1134	. . 3 wff A.xph
7	2, 4	wal 1134	. . 3 wff A.xps
8	6, 7	wi 3	. 2 wff (A.xph -> A.xps)
9	5, 8	wi 3	1 wff (A.x(ph -> ps) -> (A.xph -> A.xps))

This axiom is referenced by:  hbequid 1151  equidqe 1152  equidq 1153  ax4 1156  ax5o 1158  3ax5 5641  bnj9OLD 12165  3ax5VD 16345

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