Theorem ee022 38867

Description: e022 38866 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee022.1	|- ph
ee022.2	|- ( ps -> ( ch -> th ) )
ee022.3	|- ( ps -> ( ch -> ta ) )
ee022.4	|- ( ph -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee022	|- ( ps -> ( ch -> et ) )

Proof of Theorem ee022

Step	Hyp	Ref	Expression
1		ee022.1	. . . 4 |- ph
2	1	a1i 11	. . 3 |- ( ch -> ph )
3	2	a1i 11	. 2 |- ( ps -> ( ch -> ph ) )
4		ee022.2	. 2 |- ( ps -> ( ch -> th ) )
5		ee022.3	. 2 |- ( ps -> ( ch -> ta ) )
6		ee022.4	. 2 |- ( ph -> ( th -> ( ta -> et ) ) )
7	3, 4, 5, 6	ee222 38708	1 |- ( ps -> ( ch -> et ) )

Syntax hints:   -> wi 4

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)