Theorem entri

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

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

Proof

Step	Hyp	Ref	Expression
1		entri.1	⊢ 𝐴 ≈ 𝐵
2		entri.2	⊢ 𝐵 ≈ 𝐶
3		entr	⊢ ( ( 𝐴 ≈ 𝐵 ∧ 𝐵 ≈ 𝐶 ) → 𝐴 ≈ 𝐶 )
4	1 2 3	mp2an	⊢ 𝐴 ≈ 𝐶