Theorem bitr 689

Description: Theorem *4.22 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
bitr	⊢ (((φ ↔ ψ) ∧ (ψ ↔ χ)) → (φ ↔ χ))

Proof of Theorem bitr

Step	Hyp	Ref	Expression
1		bibi1 317	. 2 ⊢ ((φ ↔ ψ) → ((φ ↔ χ) ↔ (ψ ↔ χ)))
2	1	biimpar 471	1 ⊢ (((φ ↔ ψ) ∧ (ψ ↔ χ)) → (φ ↔ χ))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

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  df-an 360

This theorem is used by:  opelopabt  4700