Theorem ibd 451

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication.

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		ibib 448	. 2 ⊢ ((ψ → χ) ↔ (ψ → (ψ ↔ χ)))
3	1, 2	sylibr 175	1 ⊢ (φ → (ψ → χ))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  oibabs 493  sssn 1852  unblem2 3432  alephon 3671  atcv0eq 5767  atcv1 5768  atcvatlem 5770

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org