Theorem 3bitr3g

Description: More general version of 3bitr3i . Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995)

	Ref	Expression
Hypotheses	3bitr3g.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	3bitr3g.2	⊢ ( 𝜓 ↔ 𝜃 )
	3bitr3g.3	⊢ ( 𝜒 ↔ 𝜏 )
Assertion	3bitr3g	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		3bitr3g.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		3bitr3g.2	⊢ ( 𝜓 ↔ 𝜃 )
3		3bitr3g.3	⊢ ( 𝜒 ↔ 𝜏 )
4	2 1	bitr3id	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜒 ) )
5	4 3	bitrdi	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜏 ) )