Theorem lerel 8285

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 8284	. 2 |- <_ C_ ( RR* X. RR* )
2		relxp 4841	. 2 |- Rel ( RR* X. RR* )
3		relss 4819	. 2 |- ( <_ C_ ( RR* X. RR* ) -> ( Rel ( RR* X. RR* ) -> Rel <_ ) )
4	1, 2, 3	mp2 16	1 |- Rel <_

Syntax hints:   C_ wss 3201   X. cxp 4729   Rel wrel 4736   RR*cxr 8255   <_ cle 8257

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 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-dif 3203  df-in 3207  df-ss 3214  df-opab 4156  df-xp 4737  df-rel 4738  df-le 8262

This theorem is referenced by: (None)