Theorem ltrel 11324

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 11323	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5702	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5790	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3950   × cxp 5682  Rel wrel 5689  ℝ^*cxr 11295   < clt 11296

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-un 3955  df-ss 3967  df-pr 4628  df-opab 5205  df-xp 5690  df-rel 5691  df-xr 11300  df-ltxr 11301

This theorem is referenced by:  dflt2  13191  gtiso  32711