Theorem lerelxr 11353

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 11330	. 2 ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < )
2		difss 4083	. 2 ⊢ ((ℝ* × ℝ*) ∖ ◡ < ) ⊆ (ℝ* × ℝ*)
3	1, 2	eqsstri 3977	1 ⊢ ≤ ⊆ (ℝ* × ℝ*)

This proof depends on syntax axioms:   ∖ cdif 3896   ⊆ wss 3899   × cxp 5649  ^◡ccnv 5650  ℝ^*cxr 11323   < clt 11324   ≤ cle 11325

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 2733

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-dif 3902  df-ss 3916  df-le 11330

This theorem is used by:  lerel  11354  dfle2  13257  dflt2  13258  xrsle  17756  ledm  18744  lern  18745  letsr  18747  znle  21822  leex  43265  i0oii  49972  io1ii  49973