Theorem ltrel 11166

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 11165	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5632	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5720	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3900   × cxp 5612  Rel wrel 5619  ℝ^*cxr 11137   < clt 11138

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3436  df-un 3905  df-ss 3917  df-pr 4577  df-opab 5152  df-xp 5620  df-rel 5621  df-xr 11142  df-ltxr 11143

This theorem is referenced by:  dflt2  13039  gtiso  32672