Theorem lerel 11412

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 11411	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5676	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5766	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

This proof depends on syntax axioms:   ⊆ wss 3900   × cxp 5656  Rel wrel 5663  ℝ^*cxr 11381   ≤ cle 11383

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-dif 4050  df-opab 5174  df-xp 5664  df-rel 5665  df-le 11388

This theorem is used by:  dfle2  13316  dflt2  13317  ledm  18814  lern  18815  lefld  18816  letsr  18817  dvle  26382  gtiso  33391