Theorem ltrel 11198

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 11197	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5642	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5731	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3890   × cxp 5622  Rel wrel 5629  ℝ^*cxr 11169   < clt 11170

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-un 3895  df-ss 3907  df-pr 4571  df-opab 5149  df-xp 5630  df-rel 5631  df-xr 11174  df-ltxr 11175

This theorem is referenced by:  dflt2  13090  gtiso  32789