Theorem e20 38954

Description: A virtual deduction elimination rule (see syl6mpi 67). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e20.1	|- (. ph ,. ps ->. ch ).
e20.2	|- th
e20.3	|- ( ch -> ( th -> ta ) )

Assertion

Ref	Expression
e20	|- (. ph ,. ps ->. ta ).

Proof of Theorem e20

Step	Hyp	Ref	Expression
1		e20.1	. 2 |- (. ph ,. ps ->. ch ).
2		e20.2	. . 3 |- th
3	2	vd02 38823	. 2 |- (. ph ,. ps ->. th ).
4		e20.3	. 2 |- ( ch -> ( th -> ta ) )
5	1, 3, 4	e22 38896	1 |- (. ph ,. ps ->. ta ).

Syntax hints:   -> wi 4   (.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:  e20an  38955  tratrbVD  39097  onfrALTlem3VD  39123