Theorem lerel 11297

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 11296	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5673	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5762	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

This proof depends on syntax axioms:   ⊆ wss 3899   × cxp 5653  Rel wrel 5660  ℝ^*cxr 11266   ≤ cle 11268

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 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-dif 3902  df-ss 3916  df-opab 5168  df-xp 5661  df-rel 5662  df-le 11273

This theorem is used by:  dfle2  13198  dflt2  13199  ledm  18678  lern  18679  lefld  18680  letsr  18681  dvle  26234  gtiso  33173