Metamath Proof Explorer


Theorem entri

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

Ref Expression
Hypotheses entri.1 𝐴𝐵
entri.2 𝐵𝐶
Assertion entri 𝐴𝐶

Proof

Step Hyp Ref Expression
1 entri.1 𝐴𝐵
2 entri.2 𝐵𝐶
3 entr ( ( 𝐴𝐵𝐵𝐶 ) → 𝐴𝐶 )
4 1 2 3 mp2an 𝐴𝐶