Theorem int2 38831

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 38831 is ex 450. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
int2.1	|- (. (. ph ,. ps ). ->. ch ).

Assertion

Ref	Expression
int2	|- (. ph ->. ( ps -> ch ) ).

Proof of Theorem int2

Step	Hyp	Ref	Expression
1		int2.1	. . . 4 |- (. (. ph ,. ps ). ->. ch ).
2	1	dfvd2ani 38799	. . 3 |- ( ( ph /\ ps ) -> ch )
3	2	ex 450	. 2 |- ( ph -> ( ps -> ch ) )
4	3	dfvd1ir 38789	1 |- (. ph ->. ( ps -> ch ) ).

Syntax hints:   -> wi 4   (.wvd1 38785   (.wvhc2 38796

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-vd1 38786  df-vhc2 38797

This theorem is referenced by:  sspwimpVD  39155  sspwimpcfVD  39157  suctrALTcfVD  39159