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Theorem rex0 3481
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 3472 . . 3  |-  -.  x  e.  (/)
21pm2.21i 123 . 2  |-  ( x  e.  (/)  ->  -.  ph )
32nrex 2658 1  |-  -.  E. x  e.  (/)  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1696   E.wrex 2557   (/)c0 3468
This theorem is referenced by:  0iun  3975  cfeq0  7898  cfsuc  7899  pmapglb2xN  30583  elpadd0  30620
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-nul 3469
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