Theorem imbi1 472

Description: Theorem *4.84 of [WhiteheadRussell] p. 122.

Assertion

Ref	Expression
imbi1	⊢ ((φ ↔ ψ) → ((φ → χ) ↔ (ψ → χ)))

Proof of Theorem imbi1

Step	Hyp	Ref	Expression
1		id 9	. 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ))
2	1	imbi1d 465	1 ⊢ ((φ ↔ ψ) → ((φ → χ) ↔ (ψ → χ)))

Syntax hints:   → wi 2   ↔ wb 127

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

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