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Metamath Proof Explorer

Theorem entr2i

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

Ref Expression
Hypotheses entr2i.1 ⊢ 𝐴 ≈ 𝐵
entr2i.2 ⊢ 𝐵 ≈ 𝐶
Assertion entr2i 𝐶 ≈ 𝐴

Proof

Step Hyp Ref Expression
1 entr2i.1 ⊢ 𝐴 ≈ 𝐵
2 entr2i.2 ⊢ 𝐵 ≈ 𝐶
3 1 2 entri ⊢ 𝐴 ≈ 𝐶
4 3 ensymi ⊢ 𝐶 ≈ 𝐴