Theorem 3bitr4ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 2-Sep-1995)

	Ref	Expression
Hypotheses	3bitr4i.1	⊢ ( 𝜑 ↔ 𝜓 )
	3bitr4i.2	⊢ ( 𝜒 ↔ 𝜑 )
	3bitr4i.3	⊢ ( 𝜃 ↔ 𝜓 )
Assertion	3bitr4ri	⊢ ( 𝜃 ↔ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		3bitr4i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		3bitr4i.2	⊢ ( 𝜒 ↔ 𝜑 )
3		3bitr4i.3	⊢ ( 𝜃 ↔ 𝜓 )
4	1 3	bitr4i	⊢ ( 𝜑 ↔ 𝜃 )
5	2 4	bitr2i	⊢ ( 𝜃 ↔ 𝜒 )