Theorem ibd 234

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 26-Jun-2004.)

Hypothesis

Ref	Expression
ibd.1	⊢ (φ → (ψ → (ψ ↔ χ)))

Assertion

Ref	Expression
ibd	⊢ (φ → (ψ → χ))

Proof of Theorem ibd

Step	Hyp	Ref	Expression
1		ibd.1	. 2 ⊢ (φ → (ψ → (ψ ↔ χ)))
2		bi1 178	. 2 ⊢ ((ψ ↔ χ) → (ψ → χ))
3	1, 2	syli 33	1 ⊢ (φ → (ψ → χ))

Syntax hints:   → wi 4   ↔ wb 176

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 177

This theorem is referenced by:  sssn  3865