Theorem lerel 11377

Description: "Less than or equal to" is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.)

Assertion

Ref	Expression
lerel	⊢ Rel ≤

Proof of Theorem lerel

Step	Hyp	Ref	Expression
1		lerelxr 11376	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5668	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5757	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

This proof depends on syntax axioms:   ⊆ wss 3895   × cxp 5648  Rel wrel 5655  ℝ^*cxr 11346   ≤ cle 11348

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-dif 4047  df-opab 5167  df-xp 5656  df-rel 5657  df-le 11353

This theorem is used by:  dfle2  13280  dflt2  13281  ledm  18770  lern  18771  lefld  18772  letsr  18773  dvle  26333  gtiso  33342