Metamath Proof Explorer


Theorem ee112

Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee112.1
|- ( ph -> ps )
ee112.2
|- ( ph -> ch )
ee112.3
|- ( ph -> ( th -> ta ) )
ee112.4
|- ( ps -> ( ch -> ( ta -> et ) ) )
Assertion ee112
|- ( ph -> ( th -> et ) )

Proof

Step Hyp Ref Expression
1 ee112.1
 |-  ( ph -> ps )
2 ee112.2
 |-  ( ph -> ch )
3 ee112.3
 |-  ( ph -> ( th -> ta ) )
4 ee112.4
 |-  ( ps -> ( ch -> ( ta -> et ) ) )
5 1 a1d
 |-  ( ph -> ( th -> ps ) )
6 2 a1d
 |-  ( ph -> ( th -> ch ) )
7 5 6 3 4 ee222
 |-  ( ph -> ( th -> et ) )