Metamath Proof Explorer
Description: An equality transitivity inference. (Contributed by NM, 6May1994)


Ref 
Expression 

Hypotheses 
eqtr3i.1 
$${\u22a2}{A}={B}$$ 


eqtr3i.2 
$${\u22a2}{A}={C}$$ 

Assertion 
eqtr3i 
$${\u22a2}{B}={C}$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

eqtr3i.1 
$${\u22a2}{A}={B}$$ 
2 

eqtr3i.2 
$${\u22a2}{A}={C}$$ 
3 
1

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

eqtri 
$${\u22a2}{B}={C}$$ 