Metamath Proof Explorer


Theorem ee021

Description: e021 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee021.1
|- ph
ee021.2
|- ( ps -> ( ch -> th ) )
ee021.3
|- ( ps -> ta )
ee021.4
|- ( ph -> ( th -> ( ta -> et ) ) )
Assertion ee021
|- ( ps -> ( ch -> et ) )

Proof

Step Hyp Ref Expression
1 ee021.1
 |-  ph
2 ee021.2
 |-  ( ps -> ( ch -> th ) )
3 ee021.3
 |-  ( ps -> ta )
4 ee021.4
 |-  ( ph -> ( th -> ( ta -> et ) ) )
5 1 a1i
 |-  ( ch -> ph )
6 5 a1i
 |-  ( ps -> ( ch -> ph ) )
7 3 a1d
 |-  ( ps -> ( ch -> ta ) )
8 6 2 7 4 ee222
 |-  ( ps -> ( ch -> et ) )