Theorem rex0 2287

Description: Vacuous existential quantification is false.

Assertion

Ref	Expression
rex0	|- -. E.x e. (/) ph

Proof of Theorem rex0

Step	Hyp	Ref	Expression
1		noel 2280	. . 3 |- -. x e. (/)
2	1	pm2.21i 77	. 2 |- (x e. (/) -> -. ph)
3	2	nrex 1726	1 |- -. E.x e. (/) ph

Syntax hints:  -. wn 2   e. wcel 956  E.wrex 1643  (/)c0 2276

This theorem is referenced by:  0iun 2600  oarec 4186  cfeq0 4894  cfsuc 4895

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-ral 1646  df-rex 1647  df-v 1808  df-dif 2045  df-nul 2277

Copyright terms: Public domain