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Theorem supeq1i 7452
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 7450 . 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 1652   supcsup 7445
This theorem is referenced by:  supsn  7474  infmsup  9986  nninfm  10556  nn0infm  10557  supxrmnf  10896  rpsup  11247  resup  11248  gcdcom  13020  gcdass  13045  imasdsval2  13742  imasdsf1olem  18403  ovolgelb  19376  itg2seq  19634  itg2i1fseq  19647  itg2cnlem1  19653  dvfsumrlim  19915  pserdvlem2  20344  logtayl  20551  ftalem6  20860  nmopnegi  23468  nmop0  23489  nmfn0  23490  esumnul  24443  ismblfin  26247  ovoliunnfl  26248  voliunnfl  26250  itg2addnclem  26256
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-uni 4016  df-sup 7446
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