Theorem 3eqtr3ri 2262

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 2255	. 2 |- B = C
5	1, 4	eqtr3i 2255	1 |- D = C

Syntax hints:   = wceq 1398

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 1496  ax-gen 1498  ax-4 1559  ax-17 1575  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-cleq 2225

This theorem is referenced by:  indif2  3465  resdm2  5253  co01  5277  cocnvres  5287  undifdc  7184  1mhlfehlf  9456  rei  11584  resqrexlemover  11695  cos1bnd  12445  m1bits  12646  6gcd4e2  12691  3lcm2e6  12857  karatsuba  13128  cosq23lt0  15698  sincos4thpi  15705  sincos6thpi  15707  cosq34lt1  15715