Theorem ltrel 11286

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 11285	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5681	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5770	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

This proof depends on syntax axioms:   ⊆ wss 3906   × cxp 5661  Rel wrel 5668  ℝ^*cxr 11257   < clt 11258

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-un 3911  df-ss 3923  df-pr 4594  df-opab 5176  df-xp 5669  df-rel 5670  df-xr 11262  df-ltxr 11263

This theorem is used by:  dflt2  13189  gtiso  33117