Metamath Proof Explorer
Description: Substitution of equal classes into membership relation. (Contributed by NM, 21Jun1993)


Ref 
Expression 

Hypotheses 
eqeltrri.1 
$${\u22a2}{A}={B}$$ 


eqeltrri.2 
$${\u22a2}{A}\in {C}$$ 

Assertion 
eqeltrri 
$${\u22a2}{B}\in {C}$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

eqeltrri.1 
$${\u22a2}{A}={B}$$ 
2 

eqeltrri.2 
$${\u22a2}{A}\in {C}$$ 
3 
1

eqcomi 
$${\u22a2}{B}={A}$$ 
4 
3 2

eqeltri 
$${\u22a2}{B}\in {C}$$ 