Theorem ee31an 38981

Description: e31an 38980 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee31an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee31an.2	|- ( ph -> ta )
ee31an.3	|- ( ( th /\ ta ) -> et )

Assertion

Ref	Expression
ee31an	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof of Theorem ee31an

Step	Hyp	Ref	Expression
1		ee31an.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee31an.2	. . . 4 |- ( ph -> ta )
3	2	a1d 25	. . 3 |- ( ph -> ( ch -> ta ) )
4	3	a1d 25	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
5		ee31an.3	. 2 |- ( ( th /\ ta ) -> et )
6	1, 4, 5	ee33an 38963	1 |- ( ph -> ( ps -> ( ch -> et ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)