Theorem ee123 38990

Description: e123 38989 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee123.1	|- ( ph -> ps )
ee123.2	|- ( ph -> ( ch -> th ) )
ee123.3	|- ( ph -> ( ch -> ( ta -> et ) ) )
ee123.4	|- ( ps -> ( th -> ( et -> ze ) ) )

Assertion

Ref	Expression
ee123	|- ( ph -> ( ch -> ( ta -> ze ) ) )

Proof of Theorem ee123

Step	Hyp	Ref	Expression
1		ee123.1	. . . 4 |- ( ph -> ps )
2	1	a1d 25	. . 3 |- ( ph -> ( ta -> ps ) )
3	2	a1d 25	. 2 |- ( ph -> ( ch -> ( ta -> ps ) ) )
4		ee123.2	. . 3 |- ( ph -> ( ch -> th ) )
5	4	a1dd 50	. 2 |- ( ph -> ( ch -> ( ta -> th ) ) )
6		ee123.3	. 2 |- ( ph -> ( ch -> ( ta -> et ) ) )
7		ee123.4	. 2 |- ( ps -> ( th -> ( et -> ze ) ) )
8	3, 5, 6, 7	ee333 38713	1 |- ( ph -> ( ch -> ( ta -> ze ) ) )

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  df-3an 1039

This theorem is referenced by: (None)