Theorem ltrel 11037

Description: "Less than" is a relation. (Contributed by NM, 14-Oct-2005.)

Assertion

Ref	Expression
ltrel	⊢ Rel <

Proof of Theorem ltrel

Step	Hyp	Ref	Expression
1		ltrelxr 11036	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5607	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5692	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3887   × cxp 5587  Rel wrel 5594  ℝ^*cxr 11008   < clt 11009

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-un 3892  df-in 3894  df-ss 3904  df-pr 4564  df-opab 5137  df-xp 5595  df-rel 5596  df-xr 11013  df-ltxr 11014

This theorem is referenced by:  dflt2  12882  gtiso  31033