This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3eltr4i

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

Ref Expression
Hypotheses 3eltr4i.1 
|- A e. B
3eltr4i.2 
|- C = A
3eltr4i.3 
|- D = B
Assertion 3eltr4i 
|- C e. D

Proof

Step Hyp Ref Expression
1 3eltr4i.1 
 |-  A e. B
2 3eltr4i.2 
 |-  C = A
3 3eltr4i.3 
 |-  D = B
4 1 3 eleqtrri 
 |-  A e. D
5 2 4 eqeltri 
 |-  C e. D