Theorem e33 38961

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

Hypotheses

Ref	Expression
e33.1	|- (. ph ,. ps ,. ch ->. th ).
e33.2	|- (. ph ,. ps ,. ch ->. ta ).
e33.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
e33	|- (. ph ,. ps ,. ch ->. et ).

Proof of Theorem e33

Step	Hyp	Ref	Expression
1		e33.1	. 2 |- (. ph ,. ps ,. ch ->. th ).
2		e33.2	. 2 |- (. ph ,. ps ,. ch ->. ta ).
3		e33.3	. . 3 |- ( th -> ( ta -> et ) )
4	3	a1i 11	. 2 |- ( th -> ( th -> ( ta -> et ) ) )
5	1, 1, 2, 4	e333 38960	1 |- (. ph ,. ps ,. ch ->. et ).

Syntax hints:   -> wi 4   (.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:  e33an  38962  e3  38964  e03  38967  e30  38971  e13  38975  e31  38978  e23  38982  e32  38985  truniALTVD  39114  trintALTVD  39116  onfrALTlem2VD  39125