Theorem lerelxr 11290

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 11267	. 2 ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < )
2		difss 4093	. 2 ⊢ ((ℝ* × ℝ*) ∖ ◡ < ) ⊆ (ℝ* × ℝ*)
3	1, 2	eqsstri 3986	1 ⊢ ≤ ⊆ (ℝ* × ℝ*)

This proof depends on syntax axioms:   ∖ cdif 3905   ⊆ wss 3908   × cxp 5664  ^◡ccnv 5665  ℝ^*cxr 11260   < clt 11261   ≤ cle 11262

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 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-v 3460  df-dif 3911  df-ss 3925  df-le 11267

This theorem is used by:  lerel  11291  dfle2  13190  dflt2  13191  xrsle  17683  ledm  18671  lern  18672  letsr  18674  znle  21723  leex  43055  i0oii  49739  io1ii  49740