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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  3209  resdm2  4839  co01  4863  1mhlfehlf  8200  rei  9727  resqrexlemover  9837
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