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Theorem 2ralorOLD 26443
Description: Distribute quantification over "or". (Moved to 2ralor 2722 in main set.mm and may be deleted by mathbox owner, JM. --NM 29-Jan-2012.) (Contributed by Jeff Madsen, 19-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
2ralorOLD  |-  ( A. x  e.  A  A. y  e.  B  ( ph  \/  ps )  <->  ( A. x  e.  A  ph  \/  A. y  e.  B  ps ) )
Distinct variable groups:    ph, y    ps, x    y, A    x, B    x, y
Allowed substitution hints:    ph( x)    ps( y)    A( x)    B( y)

Proof of Theorem 2ralorOLD
StepHypRef Expression
1 2ralor 2722 1  |-  ( A. x  e.  A  A. y  e.  B  ( ph  \/  ps )  <->  ( A. x  e.  A  ph  \/  A. y  e.  B  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   A.wral 2556
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-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562
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