Metamath Proof Explorer


Theorem ee100

Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee100.1
|- ( ph -> ps )
ee100.2
|- ch
ee100.3
|- th
ee100.4
|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion ee100
|- ( ph -> ta )

Proof

Step Hyp Ref Expression
1 ee100.1
 |-  ( ph -> ps )
2 ee100.2
 |-  ch
3 ee100.3
 |-  th
4 ee100.4
 |-  ( ps -> ( ch -> ( th -> ta ) ) )
5 2 a1i
 |-  ( ph -> ch )
6 3 a1i
 |-  ( ph -> th )
7 1 5 6 4 syl3c
 |-  ( ph -> ta )