Theorem lerel 8136

Description: 'Less or equal to' is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.)

Assertion

Ref	Expression
lerel	|- Rel <_

Proof of Theorem lerel

Step	Hyp	Ref	Expression
1		lerelxr 8135	. 2 |- <_ C_ ( RR* X. RR* )
2		relxp 4784	. 2 |- Rel ( RR* X. RR* )
3		relss 4762	. 2 |- ( <_ C_ ( RR* X. RR* ) -> ( Rel ( RR* X. RR* ) -> Rel <_ ) )
4	1, 2, 3	mp2 16	1 |- Rel <_

Syntax hints:   C_ wss 3166   X. cxp 4673   Rel wrel 4680   RR*cxr 8106   <_ cle 8108

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-dif 3168  df-in 3172  df-ss 3179  df-opab 4106  df-xp 4681  df-rel 4682  df-le 8113

This theorem is referenced by: (None)