Theorem 0npr 9391

Description: The empty set is not a positive real. (Contributed by NM, 15-Nov-1995.) (New usage is discouraged.)

Assertion

Ref	Expression
0npr

Proof of Theorem 0npr

Step	Hyp	Ref	Expression
1		eqid 2457	. 2
2		prn0 9388	. . 3
3	2	necon2bi 2694	. 2
4	1, 3	ax-mp 5	1

Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818  c0 3784  cnp 9258

This theorem is referenced by:  genpass  9408  distrpr  9427  ltaddpr2  9434  ltapr  9444  addcanpr  9445  ltsrpr  9475  ltsosr  9492  mappsrpr  9506

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-3an 975  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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-np 9380