Theorem e2bi 45455

Description: Biconditional form of e2 45454. imbitrdi 254 is e2bi 45455 without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e2bi.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e2bi.2	⊢ (𝜒 ↔ 𝜃)

Assertion

Ref	Expression
e2bi	⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

Proof of Theorem e2bi

Step	Hyp	Ref	Expression
1		e2bi.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e2bi.2	. . 3 ⊢ (𝜒 ↔ 𝜃)
3	2	biimpi 219	. 2 ⊢ (𝜒 → 𝜃)
4	1, 3	e2 45454	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

This proof depends on syntax axioms:   ↔ wb 209  (   wvd2 45400

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 402  df-vd2 45401

This theorem is used by:  snssiALTVD  45649  eqsbc2VD  45662  en3lplem2VD  45666  onfrALTlem3VD  45709  onfrALTlem1VD  45712