Theorem 3eqtr3ri 2223

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 2216	. 2 |- B = C
5	1, 4	eqtr3i 2216	1 |- D = C

Syntax hints:   = wceq 1364

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-4 1521  ax-17 1537  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-cleq 2186

This theorem is referenced by:  indif2  3403  resdm2  5156  co01  5180  cocnvres  5190  undifdc  6980  1mhlfehlf  9200  rei  11043  resqrexlemover  11154  cos1bnd  11902  6gcd4e2  12132  3lcm2e6  12298  cosq23lt0  14968  sincos4thpi  14975  sincos6thpi  14977  cosq34lt1  14985