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Theorem rexnalOLD 2874
Description: Obsolete proof of rexnal 2873 as of 26-Nov-2019. (Contributed by NM, 21-Jan-1997.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rexnalOLD  |-  ( E. x  e.  A  -.  ph  <->  -. 
A. x  e.  A  ph )

Proof of Theorem rexnalOLD
StepHypRef Expression
1 df-rex 2781 . 2  |-  ( E. x  e.  A  -.  ph  <->  E. x ( x  e.  A  /\  -.  ph ) )
2 exanali 1715 . . 3  |-  ( E. x ( x  e.  A  /\  -.  ph ) 
<->  -.  A. x ( x  e.  A  ->  ph ) )
3 df-ral 2780 . . 3  |-  ( A. x  e.  A  ph  <->  A. x
( x  e.  A  ->  ph ) )
42, 3xchbinxr 312 . 2  |-  ( E. x ( x  e.  A  /\  -.  ph ) 
<->  -.  A. x  e.  A  ph )
51, 4bitri 252 1  |-  ( E. x  e.  A  -.  ph  <->  -. 
A. x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    /\ wa 370   A.wal 1435   E.wex 1659    e. wcel 1868   A.wral 2775   E.wrex 2776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-ral 2780  df-rex 2781
This theorem is referenced by: (None)
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