Metamath Proof Explorer

Theorem bibi1

Description: Theorem *4.86 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion bibi1 ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2 1 bibi1d ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) ) )