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Theorem supeq1i 7418
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 7416 . 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 1649   supcsup 7411
This theorem is referenced by:  supsn  7438  infmsup  9950  nninfm  10520  nn0infm  10521  supxrmnf  10860  rpsup  11210  resup  11211  gcdcom  12983  gcdass  13008  imasdsval2  13705  imasdsf1olem  18364  ovolgelb  19337  itg2seq  19595  itg2i1fseq  19608  itg2cnlem1  19614  dvfsumrlim  19876  pserdvlem2  20305  logtayl  20512  ftalem6  20821  nmopnegi  23429  nmop0  23450  nmfn0  23451  esumnul  24404  ismblfin  26154  ovoliunnfl  26155  voliunnfl  26157  itg2addnclem  26163
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ral 2679  df-rex 2680  df-rab 2683  df-uni 3984  df-sup 7412
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