Theorem 3eqtr3ri 2237

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 2230	. 2 |- B = C
5	1, 4	eqtr3i 2230	1 |- D = C

Syntax hints:   = wceq 1373

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 1471  ax-gen 1473  ax-4 1534  ax-17 1550  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-cleq 2200

This theorem is referenced by:  indif2  3425  resdm2  5192  co01  5216  cocnvres  5226  undifdc  7047  1mhlfehlf  9290  rei  11325  resqrexlemover  11436  cos1bnd  12185  m1bits  12386  6gcd4e2  12431  3lcm2e6  12597  karatsuba  12868  cosq23lt0  15420  sincos4thpi  15427  sincos6thpi  15429  cosq34lt1  15437