Theorem in3 33808

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
in3.1	|- (. ph ,. ps ,. ch ->. th ).

Assertion

Ref	Expression
in3	|- (. ph ,. ps ->. ( ch -> th ) ).

Proof of Theorem in3

Step	Hyp	Ref	Expression
1		in3.1	. . 3 |- (. ph ,. ps ,. ch ->. th ).
2	1	dfvd3i 33782	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	dfvd2ir 33776	1 |- (. ph ,. ps ->. ( ch -> th ) ).

Syntax hints:   -> wi 4   (.wvd2 33767   (.wvd3 33777

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 185  df-an 369  df-3an 973  df-vd2 33768  df-vd3 33780

This theorem is referenced by:  e223  33834  suctrALT2VD  34055  en3lplem2VD  34063  exbirVD  34072  exbiriVD  34073  rspsbc2VD  34074  tratrbVD  34081  ssralv2VD  34086  imbi12VD  34093  imbi13VD  34094  truniALTVD  34098  trintALTVD  34100  onfrALTlem2VD  34109