Theorem in2 43454

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 43434	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	2	dfvd1ir 43422	1 ⊢ (   𝜑   ▶   (𝜓 → 𝜒)   )

Syntax hints:   → wi 4  (   wvd1 43418  (   wvd2 43426

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 43419  df-vd2 43427

This theorem is referenced by:  e223  43484  trsspwALT  43667  sspwtr  43670  pwtrVD  43673  pwtrrVD  43674  snssiALTVD  43676  sstrALT2VD  43683  suctrALT2VD  43685  elex2VD  43687  elex22VD  43688  eqsbc2VD  43689  tpid3gVD  43691  en3lplem1VD  43692  en3lplem2VD  43693  3ornot23VD  43696  orbi1rVD  43697  19.21a3con13vVD  43701  exbirVD  43702  exbiriVD  43703  rspsbc2VD  43704  tratrbVD  43710  syl5impVD  43712  ssralv2VD  43715  imbi12VD  43722  imbi13VD  43723  sbcim2gVD  43724  sbcbiVD  43725  truniALTVD  43727  trintALTVD  43729  onfrALTVD  43740  relopabVD  43750  19.41rgVD  43751  hbimpgVD  43753  ax6e2eqVD  43756  ax6e2ndeqVD  43758  con3ALTVD  43765