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Theorem rex0 3798
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 3787 . . 3  |-  -.  x  e.  (/)
21pm2.21i 131 . 2  |-  ( x  e.  (/)  ->  -.  ph )
32nrex 2909 1  |-  -.  E. x  e.  (/)  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1823   E.wrex 2805   (/)c0 3783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2809  df-rex 2810  df-v 3108  df-dif 3464  df-nul 3784
This theorem is referenced by:  0iun  4372  cfeq0  8627  cfsuc  8628  cshws0  14673  meet0  15969  join0  15970  dya2iocuni  28494  eulerpartlemgh  28584  pmapglb2xN  35912  elpadd0  35949
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