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Theorem supeq1i 7216
Description: Equality inference for supremum. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
supeq1i.1  |-  B  =  C
Assertion
Ref Expression
supeq1i  |-  sup ( B ,  A ,  R )  =  sup ( C ,  A ,  R )

Proof of Theorem supeq1i
StepHypRef Expression
1 supeq1i.1 . 2  |-  B  =  C
2 supeq1 7214 . 2  |-  ( B  =  C  ->  sup ( B ,  A ,  R )  =  sup ( C ,  A ,  R ) )
31, 2ax-mp 8 1  |-  sup ( B ,  A ,  R )  =  sup ( C ,  A ,  R )
Colors of variables: wff set class
Syntax hints:    = wceq 1632   supcsup 7209
This theorem is referenced by:  supsn  7236  infmsup  9748  nninfm  10314  nn0infm  10315  supxrmnf  10652  rpsup  10986  resup  10987  gcdcom  12715  gcdass  12740  imasdsval2  13435  imasdsf1olem  17953  ovolgelb  18855  itg2seq  19113  itg2i1fseq  19126  itg2cnlem1  19132  dvfsumrlim  19394  pserdvlem2  19820  logtayl  20023  ftalem6  20331  nmopnegi  22561  nmop0  22582  nmfn0  22583  esumnul  23442  ovoliunnfl  25001  itg2addnclem  25003
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-uni 3844  df-sup 7210
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