Theorem lerelxr 11375

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 11352	. 2 ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < )
2		difss 4072	. 2 ⊢ ((ℝ* × ℝ*) ∖ ◡ < ) ⊆ (ℝ* × ℝ*)
3	1, 2	eqsstri 3954	1 ⊢ ≤ ⊆ (ℝ* × ℝ*)

This proof depends on syntax axioms:   ⊆ wss 3895   ∖ cdif 4045   × cxp 5648  ^◡ccnv 5649  ℝ^*cxr 11345   < clt 11346   ≤ cle 11347

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-dif 4047  df-le 11352

This theorem is used by:  lerel  11376  dfle2  13279  dflt2  13280  xrsle  17781  ledm  18769  lern  18770  letsr  18772  znle  21847  leex  43390  i0oii  50127  io1ii  50128