ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqtr2d Unicode version

Theorem eqtr2d 2089
Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999.)
Hypotheses
Ref Expression
eqtr2d.1  |-  ( ph  ->  A  =  B )
eqtr2d.2  |-  ( ph  ->  B  =  C )
Assertion
Ref Expression
eqtr2d  |-  ( ph  ->  C  =  A )

Proof of Theorem eqtr2d
StepHypRef Expression
1 eqtr2d.1 . . 3  |-  ( ph  ->  A  =  B )
2 eqtr2d.2 . . 3  |-  ( ph  ->  B  =  C )
31, 2eqtrd 2088 . 2  |-  ( ph  ->  A  =  C )
43eqcomd 2061 1  |-  ( ph  ->  C  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = 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:  3eqtrrd  2093  3eqtr2rd  2095  onsucmin  4261  elxp4  4836  elxp5  4837  csbopeq1a  5842  ecinxp  6212  fundmen  6317  fidifsnen  6362  addpinq1  6620  1idsr  6911  prsradd  6928  cnegexlem3  7251  cnegex  7252  submul2  7468  mulsubfacd  7487  divadddivap  7778  fzval3  9162  fzoshftral  9196  ceiqm1l  9261  flqdiv  9271  flqmod  9288  intqfrac  9289  modqcyc2  9310  modqdi  9342  frecuzrdgfn  9362  expnegzap  9454  binom2sub  9531  binom3  9534  reim  9680  mulreap  9692  addcj  9719  resqrexlemcalc1  9841  absimle  9911  clim2iser  10088  serif0  10102  divalglemnn  10230  oddpwdclemxy  10257  oddpwdclemdc  10261
  Copyright terms: Public domain W3C validator