Theorem e2bi 40959

Description: Biconditional form of e2 40958. syl6ib 253 is e2bi 40959 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 218	. 2 ⊢ (𝜒 → 𝜃)
4	1, 3	e2 40958	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )

Syntax hints:   ↔ wb 208  (   wvd2 40904

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 209  df-an 399  df-vd2 40905

This theorem is referenced by:  snssiALTVD  41154  eqsbc3rVD  41167  en3lplem2VD  41171  onfrALTlem3VD  41214  onfrALTlem1VD  41217