Theorem in3an 38836

Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a 633 is the non-virtual deduction form of in3an 38836. (Contributed by Alan Sare, 25-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
in3an	|- (. ph ,. ps ,. ch ->. ( th -> ta ) ).

Proof of Theorem in3an

Step	Hyp	Ref	Expression
1		in3an.1	. . . 4 |- (. ph ,. ps ,. ( ch /\ th ) ->. ta ).
2	1	dfvd3i 38808	. . 3 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )
3	2	exp4a 633	. 2 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	dfvd3ir 38809	1 |- (. ph ,. ps ,. ch ->. ( th -> ta ) ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd3 38803

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-3an 1039  df-vd3 38806

This theorem is referenced by:  onfrALTlem2VD  39125