Metamath Proof Explorer


Theorem in2

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis in2.1
|- (. ph ,. ps ->. ch ).
Assertion in2
|- (. ph ->. ( ps -> ch ) ).

Proof

Step Hyp Ref Expression
1 in2.1
 |-  (. ph ,. ps ->. ch ).
2 1 dfvd2i
 |-  ( ph -> ( ps -> ch ) )
3 2 dfvd1ir
 |-  (. ph ->. ( ps -> ch ) ).