Theorem 3bitr4g

Description: More general version of 3bitr4i . Useful for converting definitions in a formula. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypotheses	3bitr4g.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	3bitr4g.2	⊢ ( 𝜃 ↔ 𝜓 )
	3bitr4g.3	⊢ ( 𝜏 ↔ 𝜒 )
Assertion	3bitr4g	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		3bitr4g.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		3bitr4g.2	⊢ ( 𝜃 ↔ 𝜓 )
3		3bitr4g.3	⊢ ( 𝜏 ↔ 𝜒 )
4	2 1	syl5bb	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜒 ) )
5	4 3	bitr4di	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜏 ) )