Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  lerelxr Structured version   Unicode version

Theorem lerelxr 9697
 Description: 'Less than or equal' is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015.)
Assertion
Ref Expression
lerelxr

Proof of Theorem lerelxr
StepHypRef Expression
1 df-le 9681 . 2
2 difss 3592 . 2
31, 2eqsstri 3494 1
 Colors of variables: wff setvar class Syntax hints:   cdif 3433   wss 3436   cxp 4847  ccnv 4848  cxr 9674   clt 9675   cle 9676 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-dif 3439  df-in 3443  df-ss 3450  df-le 9681 This theorem is referenced by:  lerel  9698  dfle2  11446  dflt2  11447  ledm  16457  lern  16458  letsr  16460  xrsle  18975  znle  19093
 Copyright terms: Public domain W3C validator