Theorem 3bitr4i

Description: A chained inference from transitive law for logical equivalence. This inference is frequently used to apply a definition to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	3bitr4i.1	$$⊢\phi \leftrightarrow \psi$$
	3bitr4i.2	$$⊢\chi \leftrightarrow \phi$$
	3bitr4i.3	$$⊢\theta \leftrightarrow \psi$$
Assertion	3bitr4i	$$⊢\chi \leftrightarrow \theta$$

Proof

Step	Hyp	Ref	Expression
1		3bitr4i.1	$$⊢\phi \leftrightarrow \psi$$
2		3bitr4i.2	$$⊢\chi \leftrightarrow \phi$$
3		3bitr4i.3	$$⊢\theta \leftrightarrow \psi$$
4	1 3	bitr4i	$$⊢\phi \leftrightarrow \theta$$
5	2 4	bitri	$$⊢\chi \leftrightarrow \theta$$