Theorem lerelxr 8016

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 7994	. 2 |- <_ = ( ( RR* X. RR* ) \ `' < )
2		difss 3261	. 2 |- ( ( RR* X. RR* ) \ `' < ) C_ ( RR* X. RR* )
3	1, 2	eqsstri 3187	1 |- <_ C_ ( RR* X. RR* )

Syntax hints:   \ cdif 3126   C_ wss 3129   X. cxp 4623   `'ccnv 4624   RR*cxr 7987   < clt 7988   <_ cle 7989

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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-in 3135  df-ss 3142  df-le 7994

This theorem is referenced by:  lerel  8017