Theorem in3an

Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a is the non-virtual deduction form of in3an . (Contributed by Alan Sare, 25-Jun-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	in3an.1	|- (. ph ,. ps ,. ( ch /\ th ) ->. ta ).
Assertion	in3an	|- (. ph ,. ps ,. ch ->. ( th -> ta ) ).

Proof

Step	Hyp	Ref	Expression
1		in3an.1	|- (. ph ,. ps ,. ( ch /\ th ) ->. ta ).
2	1	dfvd3i	|- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )
3	2	exp4a	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	dfvd3ir	|- (. ph ,. ps ,. ch ->. ( th -> ta ) ).