Theorem lerelxr 8033

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

Assertion

Ref	Expression
lerelxr	|- <_ C_ ( RR* X. RR* )

Proof of Theorem lerelxr

Step	Hyp	Ref	Expression
1		df-le 8011	. 2 |- <_ = ( ( RR* X. RR* ) \ `' < )
2		difss 3273	. 2 |- ( ( RR* X. RR* ) \ `' < ) C_ ( RR* X. RR* )
3	1, 2	eqsstri 3199	1 |- <_ C_ ( RR* X. RR* )

Syntax hints:   \ cdif 3138   C_ wss 3141   X. cxp 4636   `'ccnv 4637   RR*cxr 8004   < clt 8005   <_ cle 8006

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-dif 3143  df-in 3147  df-ss 3154  df-le 8011

This theorem is referenced by:  lerel  8034