Theorem lerelxr 11399

Description: "Less than or equal to" is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015.)

Assertion

Ref	Expression
lerelxr	⊢ ≤ ⊆ (ℝ* × ℝ*)

Proof of Theorem lerelxr

Step	Hyp	Ref	Expression
1		df-le 11376	. 2 ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < )
2		difss 4075	. 2 ⊢ ((ℝ* × ℝ*) ∖ ◡ < ) ⊆ (ℝ* × ℝ*)
3	1, 2	eqsstri 3959	1 ⊢ ≤ ⊆ (ℝ* × ℝ*)

This proof depends on syntax axioms:   ⊆ wss 3900   ∖ cdif 4048   × cxp 5653  ^◡ccnv 5654  ℝ^*cxr 11369   < clt 11370   ≤ cle 11371

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-le 11376

This theorem is used by:  lerel  11400  dfle2  13303  dflt2  13304  xrsle  17805  ledm  18793  lern  18794  letsr  18796  znle  21872  leex  43490  i0oii  50239  io1ii  50240