Theorem entri

Description: A chained equinumerosity inference. (Contributed by NM, 25-Sep-2004)

	Ref	Expression
Hypotheses	entri.1	$$⊢A\approx B$$
	entri.2	$$⊢B\approx C$$
Assertion	entri	$$⊢A\approx C$$

Proof

Step	Hyp	Ref	Expression
1		entri.1	$$⊢A\approx B$$
2		entri.2	$$⊢B\approx C$$
3		entr	$$⊢\left(A\approx B\wedge B\approx C\right)\to A\approx C$$
4	1 2 3	mp2an	$$⊢A\approx C$$