Theorem e2bir 42142

Description: Right biconditional form of e2 42140. syl6ibr 251 is e2bir 42142 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 227	. 2 ⊢ (𝜒 → 𝜃)
4	1, 3	e2 42140	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

Syntax hints:   ↔ wb 205  (   wvd2 42086

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 396  df-vd2 42087

This theorem is referenced by:  trsspwALT  42327  pwtrVD  42333  eqsbc2VD  42349  tpid3gVD  42351  onfrALTlem1VD  42399