Theorem in3 31628

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 31602	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	dfvd2ir 31596	1 |- (. ph ,. ps ->. ( ch -> th ) ).

Syntax hints:   -> wi 4   (.wvd2 31587   (.wvd3 31597

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 371  df-3an 967  df-vd2 31588  df-vd3 31600

This theorem is referenced by:  e223  31654  suctrALT2VD  31869  en3lplem2VD  31877  exbirVD  31886  exbiriVD  31887  rspsbc2VD  31888  tratrbVD  31894  ssralv2VD  31899  imbi12VD  31906  imbi13VD  31907  truniALTVD  31911  trintALTVD  31913  onfrALTlem2VD  31922