Theorem ee23an 38984

Description: e23an 38983 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee23an.1	|- ( ph -> ( ps -> ch ) )
ee23an.2	|- ( ph -> ( ps -> ( th -> ta ) ) )
ee23an.3	|- ( ( ch /\ ta ) -> et )

Assertion

Ref	Expression
ee23an	|- ( ph -> ( ps -> ( th -> et ) ) )

Proof of Theorem ee23an

Step	Hyp	Ref	Expression
1		ee23an.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1dd 50	. 2 |- ( ph -> ( ps -> ( th -> ch ) ) )
3		ee23an.2	. 2 |- ( ph -> ( ps -> ( th -> ta ) ) )
4		ee23an.3	. 2 |- ( ( ch /\ ta ) -> et )
5	2, 3, 4	ee33an 38963	1 |- ( ph -> ( ps -> ( th -> 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)