Metamath Proof Explorer


Theorem ee210

Description: e210 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee210.1
|- ( ph -> ( ps -> ch ) )
ee210.2
|- ( ph -> th )
ee210.3
|- ta
ee210.4
|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion ee210
|- ( ph -> ( ps -> et ) )

Proof

Step Hyp Ref Expression
1 ee210.1
 |-  ( ph -> ( ps -> ch ) )
2 ee210.2
 |-  ( ph -> th )
3 ee210.3
 |-  ta
4 ee210.4
 |-  ( ch -> ( th -> ( ta -> et ) ) )
5 2 a1d
 |-  ( ph -> ( ps -> th ) )
6 3 a1i
 |-  ( ps -> ta )
7 6 a1i
 |-  ( ph -> ( ps -> ta ) )
8 1 5 7 4 ee222
 |-  ( ph -> ( ps -> et ) )