Theorem ee333 38713

Description: e333 38960 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee333.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee333.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
ee333.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
ee333.4	|- ( th -> ( ta -> ( et -> ze ) ) )

Assertion

Ref	Expression
ee333	|- ( ph -> ( ps -> ( ch -> ze ) ) )

Proof of Theorem ee333

Step	Hyp	Ref	Expression
1		ee333.1	. . . 4 |- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	3imp 1256	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
3		ee333.2	. . . 4 |- ( ph -> ( ps -> ( ch -> ta ) ) )
4	3	3imp 1256	. . 3 |- ( ( ph /\ ps /\ ch ) -> ta )
5		ee333.3	. . . 4 |- ( ph -> ( ps -> ( ch -> et ) ) )
6	5	3imp 1256	. . 3 |- ( ( ph /\ ps /\ ch ) -> et )
7		ee333.4	. . 3 |- ( th -> ( ta -> ( et -> ze ) ) )
8	2, 4, 6, 7	syl3c 66	. 2 |- ( ( ph /\ ps /\ ch ) -> ze )
9	8	3exp 1264	1 |- ( ph -> ( ps -> ( ch -> ze ) ) )

Syntax hints:   -> wi 4   /\ w3a 1037

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:  ee323  38714  ee123  38990