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Theorem eqtr2di 2227
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
eqtr2di.1  |-  ( ph  ->  A  =  B )
eqtr2di.2  |-  B  =  C
Assertion
Ref Expression
eqtr2di  |-  ( ph  ->  C  =  A )

Proof of Theorem eqtr2di
StepHypRef Expression
1 eqtr2di.1 . . 3  |-  ( ph  ->  A  =  B )
2 eqtr2di.2 . . 3  |-  B  =  C
31, 2eqtrdi 2226 . 2  |-  ( ph  ->  A  =  C )
43eqcomd 2183 1  |-  ( ph  ->  C  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170
This theorem is referenced by:  eqtr4id  2229  elxp4  5118  elxp5  5119  fo1stresm  6164  fo2ndresm  6165  eloprabi  6199  fo2ndf  6230  xpsnen  6823  xpassen  6832  ac6sfi  6900  undifdc  6925  ine0  8353  nn0n0n1ge2  9325  fzval2  10013  fseq1p1m1  10096  fsum2dlemstep  11444  modfsummodlemstep  11467  fprod2dlemstep  11632  ef4p  11704  sin01bnd  11767  odd2np1  11880  sqpweven  12177  2sqpwodd  12178  psmetdmdm  13863  xmetdmdm  13895  dveflem  14226  reeff1oleme  14232  abssinper  14306  lgseisenlem1  14489
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