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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