Theorem in3 36626

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 36600	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	dfvd2ir 36594	1 |- (. ph ,. ps ->. ( ch -> th ) ).

Syntax hints:   -> wi 4   (.wvd2 36585   (.wvd3 36595

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 188  df-an 372  df-3an 984  df-vd2 36586  df-vd3 36598

This theorem is referenced by:  e223  36652  suctrALT2VD  36872  en3lplem2VD  36880  exbirVD  36889  exbiriVD  36890  rspsbc2VD  36891  tratrbVD  36898  ssralv2VD  36903  imbi12VD  36910  imbi13VD  36911  truniALTVD  36915  trintALTVD  36917  onfrALTlem2VD  36926