Theorem ltrel 10781

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 10780	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5543	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5627	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3843   × cxp 5523  Rel wrel 5530  ℝ^*cxr 10752   < clt 10753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-un 3848  df-in 3850  df-ss 3860  df-pr 4519  df-opab 5093  df-xp 5531  df-rel 5532  df-xr 10757  df-ltxr 10758

This theorem is referenced by:  dflt2  12624  gtiso  30608