Theorem 3eqtrri 2191

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Hypotheses

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

Assertion

Ref	Expression
3eqtrri	|- D = A

Proof of Theorem 3eqtrri

Step	Hyp	Ref	Expression
1		3eqtri.1	. . 3 |- A = B
2		3eqtri.2	. . 3 |- B = C
3	1, 2	eqtri 2186	. 2 |- A = C
4		3eqtri.3	. 2 |- C = D
5	3, 4	eqtr2i 2187	1 |- D = A

Syntax hints:   = wceq 1343

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-4 1498  ax-17 1514  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158

This theorem is referenced by:  resindm  4926  dfdm2  5138  cofunex2g  6078  df1st2  6187  df2nd2  6188  enq0enq  7372  dfn2  9127  9p1e10  9324  0.999...  11462  pockthi  12288  sincosq3sgn  13399  sincosq4sgn  13400