Theorem vd23 38827

Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd23.1	|- (. ph ,. ps ->. ch ).

Assertion

Ref	Expression
vd23	|- (. ph ,. ps ,. th ->. ch ).

Proof of Theorem vd23

Step	Hyp	Ref	Expression
1		vd23.1	. . . 4 |- (. ph ,. ps ->. ch ).
2	1	dfvd2i 38801	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	a1dd 50	. 2 |- ( ph -> ( ps -> ( th -> ch ) ) )
4	3	dfvd3ir 38809	1 |- (. ph ,. ps ,. th ->. ch ).

Syntax hints:   (.wvd2 38793   (.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-vd2 38794  df-vd3 38806

This theorem is referenced by:  e23  38982  e32  38985  e123  38989