Theorem 3eqtr3ri 2124

Description: An inference from three chained equalities. (Contributed by NM, 15-Aug-2004.)

Hypotheses

Ref	Expression
3eqtr3i.1	|- A = B
3eqtr3i.2	|- A = C
3eqtr3i.3	|- B = D

Assertion

Ref	Expression
3eqtr3ri	|- D = C

Proof of Theorem 3eqtr3ri

Step	Hyp	Ref	Expression
1		3eqtr3i.3	. 2 |- B = D
2		3eqtr3i.1	. . 3 |- A = B
3		3eqtr3i.2	. . 3 |- A = C
4	2, 3	eqtr3i 2117	. 2 |- B = C
5	1, 4	eqtr3i 2117	1 |- D = C

Syntax hints:   = wceq 1296

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-4 1452  ax-17 1471  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-cleq 2088

This theorem is referenced by:  indif2  3259  resdm2  4955  co01  4979  cocnvres  4989  undifdc  6714  1mhlfehlf  8732  rei  10464  resqrexlemover  10574  cos1bnd  11214  6gcd4e2  11426  3lcm2e6  11581