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Theorem 3eqtr3rd 2124
Description: A deduction from three chained equalities. (Contributed by NM, 14-Jan-2006.)
Hypotheses
Ref Expression
3eqtr3d.1  |-  ( ph  ->  A  =  B )
3eqtr3d.2  |-  ( ph  ->  A  =  C )
3eqtr3d.3  |-  ( ph  ->  B  =  D )
Assertion
Ref Expression
3eqtr3rd  |-  ( ph  ->  D  =  C )

Proof of Theorem 3eqtr3rd
StepHypRef Expression
1 3eqtr3d.3 . 2  |-  ( ph  ->  B  =  D )
2 3eqtr3d.1 . . 3  |-  ( ph  ->  A  =  B )
3 3eqtr3d.2 . . 3  |-  ( ph  ->  A  =  C )
42, 3eqtr3d 2117 . 2  |-  ( ph  ->  B  =  C )
51, 4eqtr3d 2117 1  |-  ( ph  ->  D  =  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076
This theorem is referenced by:  fcofo  5503  fcof1o  5508  frecabcl  6096  nnaword  6200  enomnilem  6699  fodjuomnilem0  6707  pn0sr  7220  negeu  7576  add20  7855  2halves  8537  bcnn  10000  bcpasc  10009  resqrexlemover  10270  gcdid  10757  phiprmpw  10978
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