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Metamath Proof Explorer

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