Theorem ltrel 11410

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 11409	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5676	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5766	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

This proof depends on syntax axioms:   ⊆ wss 3900   × cxp 5656  Rel wrel 5663  ℝ^*cxr 11381   < clt 11382

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

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 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-pr 4591  df-opab 5174  df-xp 5664  df-rel 5665  df-xr 11386  df-ltxr 11387

This theorem is used by:  dflt2  13317  gtiso  33391  edompidlem  33960