Theorem lerel 11274

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 11273	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5693	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5779	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3947   × cxp 5673  Rel wrel 5680  ℝ^*cxr 11243   ≤ cle 11245

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-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-dif 3950  df-in 3954  df-ss 3964  df-opab 5210  df-xp 5681  df-rel 5682  df-le 11250

This theorem is referenced by:  dfle2  13122  dflt2  13123  ledm  18539  lern  18540  lefld  18541  letsr  18542  dvle  25515  gtiso  31909