Theorem ltrel 10301

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 10300	. 2 ⊢ < ⊆ (ℝ* × ℝ*)
2		relxp 5266	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5346	. 2 ⊢ ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
4	1, 2, 3	mp2 9	1 ⊢ Rel <

Syntax hints:   ⊆ wss 3721   × cxp 5247  Rel wrel 5254  ℝ^*cxr 10274   < clt 10275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750

This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-v 3351  df-un 3726  df-in 3728  df-ss 3735  df-pr 4317  df-opab 4845  df-xp 5255  df-rel 5256  df-xr 10279  df-ltxr 10280

This theorem is referenced by:  dflt2  12185  gtiso  29812