Theorem ee323 38714

Description: e323 38993 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee323.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee323.2	|- ( ph -> ( ps -> ta ) )
ee323.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
ee323.4	|- ( th -> ( ta -> ( et -> ze ) ) )

Assertion

Ref	Expression
ee323	|- ( ph -> ( ps -> ( ch -> ze ) ) )

Proof of Theorem ee323

Step	Hyp	Ref	Expression
1		ee323.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee323.2	. . 3 |- ( ph -> ( ps -> ta ) )
3	2	a1dd 50	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
4		ee323.3	. 2 |- ( ph -> ( ps -> ( ch -> et ) ) )
5		ee323.4	. 2 |- ( th -> ( ta -> ( et -> ze ) ) )
6	1, 3, 4, 5	ee333 38713	1 |- ( ph -> ( ps -> ( ch -> 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:  e323  38993  trintALT  39117