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	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	3bitr4g.2	$$⊢\theta \leftrightarrow \psi$$
	3bitr4g.3	$$⊢\tau \leftrightarrow \chi$$
Assertion	3bitr4g	$$⊢\phi \to \left(\theta \leftrightarrow \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		3bitr4g.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		3bitr4g.2	$$⊢\theta \leftrightarrow \psi$$
3		3bitr4g.3	$$⊢\tau \leftrightarrow \chi$$
4	2 1	syl5bb	$$⊢\phi \to \left(\theta \leftrightarrow \chi \right)$$
5	4 3	bitr4di	$$⊢\phi \to \left(\theta \leftrightarrow \tau \right)$$