Theorem bitr4i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993)

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

Proof

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