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Metamath Proof Explorer

Theorem entr3i

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

Ref Expression
Hypotheses entr3i.1 ⊢ 𝐴 ≈ 𝐵
entr3i.2 ⊢ 𝐴 ≈ 𝐶
Assertion entr3i 𝐵 ≈ 𝐶

Proof

Step Hyp Ref Expression
1 entr3i.1 ⊢ 𝐴 ≈ 𝐵
2 entr3i.2 ⊢ 𝐴 ≈ 𝐶
3 1 ensymi ⊢ 𝐵 ≈ 𝐴
4 3 2 entri ⊢ 𝐵 ≈ 𝐶