Theorem 3eqtr3ri 2268

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 2261	. 2 |- B = C
5	1, 4	eqtr3i 2261	1 |- D = C

This proof depends on syntax axioms:   = wceq 1402

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-4 1563  ax-17 1579  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231

This theorem is used by:  indif2  3475  resdm2  5281  co01  5305  cocnvres  5315  undifdc  7235  1mhlfehlf  9534  rei  11687  resqrexlemover  11798  cos1bnd  12551  m1bits  12752  6gcd4e2  12797  3lcm2e6  12964  karatsuba  13239  ballotfilemth  13339  cosq23lt0  16060  sincos4thpi  16067  sincos6thpi  16069  cosq34lt1  16078  cht3  16277  bclbnd  16307  bposlem8  16318