Metamath Proof Explorer

Theorem nn0ssxnn0

Description: The standard nonnegative integers are a subset of the extended nonnegative integers. (Contributed by AV, 10-Dec-2020)

Ref Expression
Assertion nn0ssxnn0 
|- NN0 C_ NN0*

Proof

Step Hyp Ref Expression
1 ssun1 
 |-  NN0 C_ ( NN0 u. { +oo } )
2 df-xnn0 
 |-  NN0* = ( NN0 u. { +oo } )
3 1 2 sseqtrri 
 |-  NN0 C_ NN0*