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Theorem ralunOLD 26342
Description: Restricted quantification over union. (Moved to ralun 3357 in main set.mm and may be deleted by mathbox owner, JM. --NM 29-Jan-2012.) (Contributed by Jeff Madsen, 2-Sep-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ralunOLD  |-  ( ( A. x  e.  A  ph 
/\  A. x  e.  B  ph )  ->  A. x  e.  ( A  u.  B
) ph )
Distinct variable groups:    x, A    x, B
Allowed substitution hint:    ph( x)

Proof of Theorem ralunOLD
StepHypRef Expression
1 ralun 3357 1  |-  ( ( A. x  e.  A  ph 
/\  A. x  e.  B  ph )  ->  A. x  e.  ( A  u.  B
) ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wral 2543    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-v 2790  df-un 3157
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