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Theorem rex0 3468
Description: Vacuous existential quantification is false. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
rex0  |-  -.  E. x  e.  (/)  ph

Proof of Theorem rex0
StepHypRef Expression
1 noel 3459 . . 3  |-  -.  x  e.  (/)
21pm2.21i 123 . 2  |-  ( x  e.  (/)  ->  -.  ph )
32nrex 2645 1  |-  -.  E. x  e.  (/)  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1684   E.wrex 2544   (/)c0 3455
This theorem is referenced by:  0iun  3959  cfeq0  7882  cfsuc  7883  pmapglb2xN  29961  elpadd0  29998
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-rex 2549  df-v 2790  df-dif 3155  df-nul 3456
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