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Metamath Proof Explorer

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