Theorem ltrel 11371

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 11370	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5669	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5758	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

This proof depends on syntax axioms:   ⊆ wss 3899   × cxp 5649  Rel wrel 5656  ℝ^*cxr 11342   < clt 11343

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 2147  ax-9 2155  ax-ext 2733

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 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-un 3904  df-ss 3916  df-pr 4587  df-opab 5168  df-xp 5657  df-rel 5658  df-xr 11347  df-ltxr 11348

This theorem is used by:  dflt2  13277  gtiso  33294