Theorem lerel 11209

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 11208	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5649	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5738	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3889   × cxp 5629  Rel wrel 5636  ℝ^*cxr 11178   ≤ cle 11180

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-dif 3892  df-ss 3906  df-opab 5148  df-xp 5637  df-rel 5638  df-le 11185

This theorem is referenced by:  dfle2  13098  dflt2  13099  ledm  18556  lern  18557  lefld  18558  letsr  18559  dvle  25974  gtiso  32774