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Theorem rabxmOLD 26352
Description: Law of excluded middle, in terms of restricted class abstractions. (Contributed by Jeff Madsen, 20-Jun-2011.) (Moved to rabxm 3477 in main set.mm and may be deleted by mathbox owner, JM. --NM 10-Nov-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rabxmOLD  |-  A  =  ( { x  e.  A  |  ph }  u.  { x  e.  A  |  -.  ph } )
Distinct variable group:    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem rabxmOLD
StepHypRef Expression
1 rabxm 3477 1  |-  A  =  ( { x  e.  A  |  ph }  u.  { x  e.  A  |  -.  ph } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1623   {crab 2547    u. cun 3150
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rab 2552  df-v 2790  df-un 3157
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