Theorem el1 38853

Description: A Virtual deduction elimination rule. syl 17 is el1 38853 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
el1.1	|- (. ph ->. ps ).
el1.2	|- ( ps -> ch )

Assertion

Ref	Expression
el1	|- (. ph ->. ch ).

Proof of Theorem el1

Step	Hyp	Ref	Expression
1		el1.1	. . . 4 |- (. ph ->. ps ).
2	1	in1 38787	. . 3 |- ( ph -> ps )
3		el1.2	. . 3 |- ( ps -> ch )
4	2, 3	syl 17	. 2 |- ( ph -> ch )
5	4	dfvd1ir 38789	1 |- (. ph ->. ch ).

Syntax hints:   -> wi 4   (.wvd1 38785

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-vd1 38786

This theorem is referenced by:  sspwimpVD  39155  sspwimpcfVD  39157  suctrALTcfVD  39159