Theorem bi2imp 45225

Description: Importation inference similar to imp 412, except both implications of the hypothesis are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi2imp.1	⊢ (𝜑 ↔ (𝜓 ↔ 𝜒))

Assertion

Ref	Expression
bi2imp	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem bi2imp

Step	Hyp	Ref	Expression
1		bi2imp.1	. . 3 ⊢ (𝜑 ↔ (𝜓 ↔ 𝜒))
2	1	biimpi 219	. 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒))
3	2	biimpa 482	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

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

This theorem is used by: (None)