Theorem rpgt0t 6287

Description: A positive real is greater than zero. (Contributed by FL, 27-Dec-2007.)

Assertion

Ref	Expression
rpgt0t	|- (A e. RR+ -> 0 < A)

Proof of Theorem rpgt0t

Step	Hyp	Ref	Expression
1		elrp 6283	. 2 |- (A e. RR+ <-> (A e. RR /\ 0 < A))
2	1	pm3.27bi 326	1 |- (A e. RR+ -> 0 < A)

Syntax hints:   -> wi 3   e. wcel 960   class class class wbr 2624  RRcr 5245  0cc0 5246  RR+crp 5312   < clt 5498

This theorem is referenced by:  rpge0t 6288  rpne0t 6289  rpdivclt 6293  rpsqrclt 6716  ivthlem6 7286  ivthlem7 7287  pipos 8673  reeflogt 8756  relogeftb 8760

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-rab 1655  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625  df-rp 6282

Copyright terms: Public domain