Theorem in2 43351

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
in2.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )

Assertion

Ref	Expression
in2	⊢ (   𝜑   ▶   (𝜓 → 𝜒)   )

Proof of Theorem in2

Step	Hyp	Ref	Expression
1		in2.1	. . 3 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2	1	dfvd2i 43331	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	2	dfvd1ir 43319	1 ⊢ (   𝜑   ▶   (𝜓 → 𝜒)   )

Syntax hints:   → wi 4  (   wvd1 43315  (   wvd2 43323

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 206  df-an 397  df-vd1 43316  df-vd2 43324

This theorem is referenced by:  e223  43381  trsspwALT  43564  sspwtr  43567  pwtrVD  43570  pwtrrVD  43571  snssiALTVD  43573  sstrALT2VD  43580  suctrALT2VD  43582  elex2VD  43584  elex22VD  43585  eqsbc2VD  43586  tpid3gVD  43588  en3lplem1VD  43589  en3lplem2VD  43590  3ornot23VD  43593  orbi1rVD  43594  19.21a3con13vVD  43598  exbirVD  43599  exbiriVD  43600  rspsbc2VD  43601  tratrbVD  43607  syl5impVD  43609  ssralv2VD  43612  imbi12VD  43619  imbi13VD  43620  sbcim2gVD  43621  sbcbiVD  43622  truniALTVD  43624  trintALTVD  43626  onfrALTVD  43637  relopabVD  43647  19.41rgVD  43648  hbimpgVD  43650  ax6e2eqVD  43653  ax6e2ndeqVD  43655  con3ALTVD  43662