Theorem in2an

Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd is the non-virtual deduction form of in2an . (Contributed by Alan Sare, 30-Jun-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	in2an.1	|- (. ph ,. ( ps /\ ch ) ->. th ).
Assertion	in2an	|- (. ph ,. ps ->. ( ch -> th ) ).

Proof

Step	Hyp	Ref	Expression
1		in2an.1	|- (. ph ,. ( ps /\ ch ) ->. th ).
2	1	dfvd2i	|- ( ph -> ( ( ps /\ ch ) -> th ) )
3	2	expd	|- ( ph -> ( ps -> ( ch -> th ) ) )
4	3	dfvd2ir	|- (. ph ,. ps ->. ( ch -> th ) ).