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Theorem rex0 3799
Description: Vacuous existential quantification is false. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
rex0

Proof of Theorem rex0
StepHypRef Expression
1 noel 3788 . . 3
21pm2.21i 131 . 2
32nrex 2912 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  e.wcel 1818  E.wrex 2808   c0 3784
This theorem is referenced by:  0iun  4387  cfeq0  8657  cfsuc  8658  cshws0  14586  meet0  15767  join0  15768  dya2iocuni  28254  eulerpartlemgh  28317  pmapglb2xN  35496  elpadd0  35533
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-nul 3785
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