Theorem e13an 16617

Description: A virtual deduction elimination rule.

Hypotheses

Ref	Expression
e13an.1	|- . ph   ⊢   ps .
e13an.2	|- . ph, ch, th   ⊢   ta .
e13an.3	|- ((ps /\ ta) -> et)

Assertion

Ref	Expression
e13an	|- . ph, ch, th   ⊢   et .

Proof of Theorem e13an

Step	Hyp	Ref	Expression
1		e13an.1	. 2 |- . ph   ⊢   ps .
2		e13an.2	. 2 |- . ph, ch, th   ⊢   ta .
3		e13an.3	. . 3 |- ((ps /\ ta) -> et)
4	3	ex 402	. 2 |- (ps -> (ta -> et))
5	1, 2, 4	e13 16616	1 |- . ph, ch, th   ⊢   et .

Syntax hints:   -> wi 3   /\ wa 240   . vd1 16479   . vd3 16493

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-3an 860  df-vd1 16480  df-vd3 16494

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