Theorem e22 39417

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e22.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e22.2	⊢ (   𝜑   ,   𝜓   ▶   𝜃   )
e22.3	⊢ (𝜒 → (𝜃 → 𝜏))

Assertion

Ref	Expression
e22	⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e22

Step	Hyp	Ref	Expression
1		e22.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e22.2	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )
3		e22.3	. . 3 ⊢ (𝜒 → (𝜃 → 𝜏))
4	3	a1i 11	. 2 ⊢ (𝜒 → (𝜒 → (𝜃 → 𝜏)))
5	1, 1, 2, 4	e222 39382	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd2 39314

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 197  df-an 385  df-vd2 39315

This theorem is referenced by:  e22an  39418  e02  39443  e12  39472  e20  39475  e21  39478  sspwtr  39569  pwtrVD  39577  pwtrrVD  39578  elex22VD  39592  tpid3gVD  39595  en3lplem2VD  39597  imbi12VD  39627  truniALTVD  39632  trintALTVD  39634  onfrALTlem3VD  39641  onfrALTlem2VD  39643  ax6e2eqVD  39661  ax6e2ndeqVD  39663  sb5ALTVD  39667