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Theorem 3reeanvOLD 26346
Description: Rearrange three existential quantifiers. (Moved to 3reeanv 2708 in main set.mm and may be deleted by mathbox owner, JM. --NM 21-Mar-2013.) (Contributed by Jeff Madsen, 11-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3reeanvOLD  |-  ( E. x  e.  A  E. y  e.  B  E. z  e.  C  ( ph  /\  ps  /\  ch ) 
<->  ( E. x  e.  A  ph  /\  E. y  e.  B  ps  /\ 
E. z  e.  C  ch ) )
Distinct variable groups:    ph, y, z    ps, x, z    ch, x, y    y, A    x, B, z    x, C, y
Allowed substitution hints:    ph( x)    ps( y)    ch( z)    A( x, z)    B( y)    C( z)

Proof of Theorem 3reeanvOLD
StepHypRef Expression
1 3reeanv 2708 1  |-  ( E. x  e.  A  E. y  e.  B  E. z  e.  C  ( ph  /\  ps  /\  ch ) 
<->  ( E. x  e.  A  ph  /\  E. y  e.  B  ps  /\ 
E. z  e.  C  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w3a 934   E.wrex 2544
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-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549
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