Theorem imbi2 314

Description: Theorem *4.85 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)

Assertion

Ref	Expression
imbi2	⊢ ((φ ↔ ψ) → ((χ → φ) ↔ (χ → ψ)))

Proof of Theorem imbi2

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ))
2	1	imbi2d 307	1 ⊢ ((φ ↔ ψ) → ((χ → φ) ↔ (χ → ψ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  3impexpbicom  1367