Metamath Proof Explorer


Theorem e3

Description: Meta-connective form of syl8 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e3.1
|- (. ph ,. ps ,. ch ->. th ).
e3.2
|- ( th -> ta )
Assertion e3
|- (. ph ,. ps ,. ch ->. ta ).

Proof

Step Hyp Ref Expression
1 e3.1
 |-  (. ph ,. ps ,. ch ->. th ).
2 e3.2
 |-  ( th -> ta )
3 2 a1i
 |-  ( th -> ( th -> ta ) )
4 1 1 3 e33
 |-  (. ph ,. ps ,. ch ->. ta ).