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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  4905  dfdm2  5117  cofunex2g  6054  df1st2  6160  df2nd2  6161  enq0enq  7334  dfn2  9086  9p1e10  9280  0.999...  11400  sincosq3sgn  13109  sincosq4sgn  13110
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