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	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	3bitr3g.2	$$⊢\psi \leftrightarrow \theta$$
	3bitr3g.3	$$⊢\chi \leftrightarrow \tau$$
Assertion	3bitr3g	$$⊢\phi \to \left(\theta \leftrightarrow \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		3bitr3g.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		3bitr3g.2	$$⊢\psi \leftrightarrow \theta$$
3		3bitr3g.3	$$⊢\chi \leftrightarrow \tau$$
4	2 1	bitr3id	$$⊢\phi \to \left(\theta \leftrightarrow \chi \right)$$
5	4 3	bitrdi	$$⊢\phi \to \left(\theta \leftrightarrow \tau \right)$$