Theorem e21 38957

Description: A virtual deduction elimination rule (see syl6ci 71). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e21.1	|- (. ph ,. ps ->. ch ).
e21.2	|- (. ph ->. th ).
e21.3	|- ( ch -> ( th -> ta ) )

Assertion

Ref	Expression
e21	|- (. ph ,. ps ->. ta ).

Proof of Theorem e21

Step	Hyp	Ref	Expression
1		e21.1	. 2 |- (. ph ,. ps ->. ch ).
2		e21.2	. . 3 |- (. ph ->. th ).
3	2	vd12 38825	. 2 |- (. ph ,. ps ->. th ).
4		e21.3	. 2 |- ( ch -> ( th -> ta ) )
5	1, 3, 4	e22 38896	1 |- (. ph ,. ps ->. ta ).

Syntax hints:   -> wi 4   (.wvd1 38785   (.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-vd1 38786  df-vd2 38794

This theorem is referenced by:  e21an  38958  en3lplem1VD  39078  exbiriVD  39089  syl5impVD  39099  sbcim2gVD  39111  onfrALTlem3VD  39123  onfrALTlem2VD  39125  hbimpgVD  39140  ax6e2eqVD  39143  vk15.4jVD  39150