Theorem ee13an 16618

Description: e13an 16617 without virtual deductions.

Hypotheses

Ref	Expression
ee13an.1	|- (ph -> ps)
ee13an.2	|- (ph -> (ch -> (th -> ta)))
ee13an.3	|- ((ps /\ ta) -> et)

Assertion

Ref	Expression
ee13an	|- (ph -> (ch -> (th -> et)))

Proof of Theorem ee13an

Step	Hyp	Ref	Expression
1		ee13an.1	. 2 |- (ph -> ps)
2		ee13an.2	. 2 |- (ph -> (ch -> (th -> ta)))
3		ee13an.3	. . 3 |- ((ps /\ ta) -> et)
4	3	ex 402	. 2 |- (ps -> (ta -> et))
5	1, 2, 4	ee13 1275	1 |- (ph -> (ch -> (th -> et)))

Syntax hints:   -> wi 3   /\ wa 240

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

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