Metamath Proof Explorer


Theorem ee31an

Description: e31an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee31an.1
|- ( ph -> ( ps -> ( ch -> th ) ) )
ee31an.2
|- ( ph -> ta )
ee31an.3
|- ( ( th /\ ta ) -> et )
Assertion ee31an
|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step Hyp Ref Expression
1 ee31an.1
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
2 ee31an.2
 |-  ( ph -> ta )
3 ee31an.3
 |-  ( ( th /\ ta ) -> et )
4 2 a1d
 |-  ( ph -> ( ch -> ta ) )
5 4 a1d
 |-  ( ph -> ( ps -> ( ch -> ta ) ) )
6 1 5 3 ee33an
 |-  ( ph -> ( ps -> ( ch -> et ) ) )