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Metamath Proof Explorer

Theorem eqeltrrdi

Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)

Ref Expression
Hypotheses eqeltrrdi.1 
|- ( ph -> B = A )
eqeltrrdi.2 
|- B e. C
Assertion eqeltrrdi 
|- ( ph -> A e. C )

Proof

Step Hyp Ref Expression
1 eqeltrrdi.1 
 |-  ( ph -> B = A )
2 eqeltrrdi.2 
 |-  B e. C
3 1 eqcomd 
 |-  ( ph -> A = B )
4 3 2 eqeltrdi 
 |-  ( ph -> A e. C )