Theorem ee121 38711

Description: e121 38881 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee121.1	|- ( ph -> ps )
ee121.2	|- ( ph -> ( ch -> th ) )
ee121.3	|- ( ph -> ta )
ee121.4	|- ( ps -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee121	|- ( ph -> ( ch -> et ) )

Proof of Theorem ee121

Step	Hyp	Ref	Expression
1		ee121.1	. . 3 |- ( ph -> ps )
2	1	a1d 25	. 2 |- ( ph -> ( ch -> ps ) )
3		ee121.2	. 2 |- ( ph -> ( ch -> th ) )
4		ee121.3	. . 3 |- ( ph -> ta )
5	4	a1d 25	. 2 |- ( ph -> ( ch -> ta ) )
6		ee121.4	. 2 |- ( ps -> ( th -> ( ta -> et ) ) )
7	2, 3, 5, 6	ee222 38708	1 |- ( ph -> ( 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:  tratrb  38746