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