Theorem ltrel 11275

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 11274	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5694	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5781	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3948   × cxp 5674  Rel wrel 5681  ℝ^*cxr 11246   < clt 11247

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-un 3953  df-in 3955  df-ss 3965  df-pr 4631  df-opab 5211  df-xp 5682  df-rel 5683  df-xr 11251  df-ltxr 11252

This theorem is referenced by:  dflt2  13126  gtiso  31917