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Metamath Proof Explorer

Theorem 3eltr3i

Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017)

Ref Expression
Hypotheses 3eltr3i.1 
|- A e. B
3eltr3i.2 
|- A = C
3eltr3i.3 
|- B = D
Assertion 3eltr3i 
|- C e. D

Proof

Step Hyp Ref Expression
1 3eltr3i.1 
 |-  A e. B
2 3eltr3i.2 
 |-  A = C
3 3eltr3i.3 
 |-  B = D
4 1 3 eleqtri 
 |-  A e. D
5 2 4 eqeltrri 
 |-  C e. D