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Theorem 3eqtr3rd 2078
Description: A deduction from three chained equalities. (Contributed by NM, 14-Jan-2006.)
Hypotheses
Ref Expression
3eqtr3d.1
3eqtr3d.2  C
3eqtr3d.3  D
Assertion
Ref Expression
3eqtr3rd  D  C

Proof of Theorem 3eqtr3rd
StepHypRef Expression
1 3eqtr3d.3 . 2  D
2 3eqtr3d.1 . . 3
3 3eqtr3d.2 . . 3  C
42, 3eqtr3d 2071 . 2  C
51, 4eqtr3d 2071 1  D  C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030
This theorem is referenced by:  fcofo  5367  fcof1o  5372  nnaword  6020  pn0sr  6699  negeu  6999  add20  7264  2halves  7931
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