Theorem lerelxr 11300

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 11277	. 2 ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < )
2		difss 4086	. 2 ⊢ ((ℝ* × ℝ*) ∖ ◡ < ) ⊆ (ℝ* × ℝ*)
3	1, 2	eqsstri 3980	1 ⊢ ≤ ⊆ (ℝ* × ℝ*)

This proof depends on syntax axioms:   ∖ cdif 3899   ⊆ wss 3902   × cxp 5657  ^◡ccnv 5658  ℝ^*cxr 11270   < clt 11271   ≤ cle 11272

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 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-dif 3905  df-ss 3919  df-le 11277

This theorem is used by:  lerel  11301  dfle2  13202  dflt2  13203  xrsle  17696  ledm  18684  lern  18685  letsr  18687  znle  21755  leex  43121  i0oii  49854  io1ii  49855