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Theorem nfrexOLD 2890
Description: Obsolete proof of nfrex 2889 as of 30-Dec-2019. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfrex.1  |-  F/_ x A
nfrex.2  |-  F/ x ph
Assertion
Ref Expression
nfrexOLD  |-  F/ x E. y  e.  A  ph

Proof of Theorem nfrexOLD
StepHypRef Expression
1 dfrex2 2877 . 2  |-  ( E. y  e.  A  ph  <->  -. 
A. y  e.  A  -.  ph )
2 nfrex.1 . . . 4  |-  F/_ x A
3 nfrex.2 . . . . 5  |-  F/ x ph
43nfn 1957 . . . 4  |-  F/ x  -.  ph
52, 4nfral 2812 . . 3  |-  F/ x A. y  e.  A  -.  ph
65nfn 1957 . 2  |-  F/ x  -.  A. y  e.  A  -.  ph
71, 6nfxfr 1693 1  |-  F/ x E. y  e.  A  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   F/wnf 1664   F/_wnfc 2571   A.wral 2776   E.wrex 2777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401
This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ral 2781  df-rex 2782
This theorem is referenced by: (None)
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