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Metamath Proof Explorer

Theorem eqneltri

Description: If a class is not an element of another class, an equal class is also not an element. (Contributed by Glauco Siliprandi, 3-Jan-2021)

Ref Expression
Hypotheses eqneltri.1 
|- A = B
eqneltri.2 
|- -. B e. C
Assertion eqneltri 
|- -. A e. C

Proof

Step Hyp Ref Expression
1 eqneltri.1 
 |-  A = B
2 eqneltri.2 
 |-  -. B e. C
3 1 eleq1i 
 |-  ( A e. C <-> B e. C )
4 2 3 mtbir 
 |-  -. A e. C