Theorem ltrel 11313

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 11312	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5696	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5783	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3944   × cxp 5676  Rel wrel 5683  ℝ^*cxr 11284   < clt 11285

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-un 3949  df-ss 3961  df-pr 4633  df-opab 5212  df-xp 5684  df-rel 5685  df-xr 11289  df-ltxr 11290

This theorem is referenced by:  dflt2  13167  gtiso  32567