Metamath Proof Explorer


Theorem e23

Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e23.1
|- (. ph ,. ps ->. ch ).
e23.2
|- (. ph ,. ps ,. th ->. ta ).
e23.3
|- ( ch -> ( ta -> et ) )
Assertion e23
|- (. ph ,. ps ,. th ->. et ).

Proof

Step Hyp Ref Expression
1 e23.1
 |-  (. ph ,. ps ->. ch ).
2 e23.2
 |-  (. ph ,. ps ,. th ->. ta ).
3 e23.3
 |-  ( ch -> ( ta -> et ) )
4 1 vd23
 |-  (. ph ,. ps ,. th ->. ch ).
5 4 2 3 e33
 |-  (. ph ,. ps ,. th ->. et ).