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Theorem 3eqtrri 2081
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 2076 . 2 𝐴 = 𝐶
4 3eqtri.3 . 2 𝐶 = 𝐷
53, 4eqtr2i 2077 1 𝐷 = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1259
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049
This theorem is referenced by:  dfdm2  4880  cofunex2g  5767  df1st2  5868  df2nd2  5869  enq0enq  6587  dfn2  8252  9p1e10  8429
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