Metamath Proof Explorer


Theorem 3eqtr4i

Description: An inference from three chained equalities. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 25-May-2011)

Ref Expression
Hypotheses 3eqtr4i.1 A=B
3eqtr4i.2 C=A
3eqtr4i.3 D=B
Assertion 3eqtr4i C=D

Proof

Step Hyp Ref Expression
1 3eqtr4i.1 A=B
2 3eqtr4i.2 C=A
3 3eqtr4i.3 D=B
4 3 1 eqtr4i D=A
5 2 4 eqtr4i C=D