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Theorem 3eqtrri 2183
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
StepHypRef Expression
1 3eqtri.1 . . 3  |-  A  =  B
2 3eqtri.2 . . 3  |-  B  =  C
31, 2eqtri 2178 . 2  |-  A  =  C
4 3eqtri.3 . 2  |-  C  =  D
53, 4eqtr2i 2179 1  |-  D  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1335
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 1427  ax-gen 1429  ax-4 1490  ax-17 1506  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-cleq 2150
This theorem is referenced by:  resindm  4907  dfdm2  5119  cofunex2g  6057  df1st2  6163  df2nd2  6164  enq0enq  7346  dfn2  9098  9p1e10  9292  0.999...  11413  sincosq3sgn  13136  sincosq4sgn  13137
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