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Theorem supeq2OLD 26521
Description: Equality theorem for supremum. (Moved to supeq2 7217 in main set.mm and may be deleted by mathbox owner, JM. --NM 24-Sep-2013.) (Contributed by Jeff Madsen, 2-Sep-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
supeq2OLD  |-  ( B  =  C  ->  sup ( A ,  B ,  R )  =  sup ( A ,  C ,  R ) )

Proof of Theorem supeq2OLD
StepHypRef Expression
1 supeq2 7217 1  |-  ( B  =  C  ->  sup ( A ,  B ,  R )  =  sup ( A ,  C ,  R ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   supcsup 7209
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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