Theorem entr4i

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

	Ref	Expression
Hypotheses	entr4i.1	⊢ 𝐴 ≈ 𝐵
	entr4i.2	⊢ 𝐶 ≈ 𝐵
Assertion	entr4i	⊢ 𝐴 ≈ 𝐶

Proof

Step	Hyp	Ref	Expression
1		entr4i.1	⊢ 𝐴 ≈ 𝐵
2		entr4i.2	⊢ 𝐶 ≈ 𝐵
3	2	ensymi	⊢ 𝐵 ≈ 𝐶
4	1 3	entri	⊢ 𝐴 ≈ 𝐶