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Theorem 3eqtr3ri 2085
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
StepHypRef Expression
1 3eqtr3i.3 . 2 𝐵 = 𝐷
2 3eqtr3i.1 . . 3 𝐴 = 𝐵
3 3eqtr3i.2 . . 3 𝐴 = 𝐶
42, 3eqtr3i 2078 . 2 𝐵 = 𝐶
51, 4eqtr3i 2078 1 𝐷 = 𝐶
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:  indif2  3208  resdm2  4838  co01  4862  1mhlfehlf  8199  rei  9726  resqrexlemover  9836
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