Theorem bibi1 317

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

Assertion

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

Proof of Theorem bibi1

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ))
2	1	bibi1d 310	1 ⊢ ((φ ↔ ψ) → ((φ ↔ χ) ↔ (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:  bitr  689  sbeqalb  3099