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Theorem rex0 3633
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 3624 . . 3  |-  -.  x  e.  (/)
21pm2.21i 125 . 2  |-  ( x  e.  (/)  ->  -.  ph )
32nrex 2800 1  |-  -.  E. x  e.  (/)  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1725   E.wrex 2698   (/)c0 3620
This theorem is referenced by:  0iun  4140  cfeq0  8128  cfsuc  8129  dya2iocuni  24625  pmapglb2xN  30506  elpadd0  30543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-nul 3621
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