Theorem in2an 38833

Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd 452 is the non-virtual deduction form of in2an 38833. (Contributed by Alan Sare, 30-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
in2an	|- (. ph ,. ps ->. ( ch -> th ) ).

Proof of Theorem in2an

Step	Hyp	Ref	Expression
1		in2an.1	. . . 4 |- (. ph ,. ( ps /\ ch ) ->. th ).
2	1	dfvd2i 38801	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	2	expd 452	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
4	3	dfvd2ir 38802	1 |- (. ph ,. ps ->. ( ch -> th ) ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd2 38793

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-vd2 38794

This theorem is referenced by:  onfrALTVD  39127