Theorem e2bir 45370

Description: Right biconditional form of e2 45368. imbitrrdi 255 is e2bir 45370 without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e2bir.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e2bir.2	⊢ (𝜃 ↔ 𝜒)

Assertion

Ref	Expression
e2bir	⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

Proof of Theorem e2bir

Step	Hyp	Ref	Expression
1		e2bir.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e2bir.2	. . 3 ⊢ (𝜃 ↔ 𝜒)
3	2	biimpri 231	. 2 ⊢ (𝜒 → 𝜃)
4	1, 3	e2 45368	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

This proof depends on syntax axioms:   ↔ wb 209  (   wvd2 45314

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-vd2 45315

This theorem is used by:  trsspwALT  45554  pwtrVD  45560  eqsbc2VD  45576  tpid3gVD  45578  onfrALTlem1VD  45626