Theorem e000 16634

Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 16634 is the virtual deduction form.

Hypotheses

Ref	Expression
e000.1	|- ph
e000.2	|- ps
e000.3	|- ch
e000.4	|- (ph -> (ps -> (ch -> th)))

Assertion

Ref	Expression
e000	|- th

Proof of Theorem e000

Step	Hyp	Ref	Expression
1		e000.3	. 2 |- ch
2		e000.1	. . 3 |- ph
3		e000.2	. . 3 |- ps
4		e000.4	. . 3 |- (ph -> (ps -> (ch -> th)))
5	2, 3, 4	mp2 54	. 2 |- (ch -> th)
6	1, 5	ax-mp 7	1 |- th

Syntax hints:   -> wi 3

This theorem was proved from axioms:  ax-mp 7

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