Theorem 0xnn0 9364

Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
0xnn0	|- 0 e. NN0*

Proof of Theorem 0xnn0

Step	Hyp	Ref	Expression
1		nn0ssxnn0 9361	. 2 |- NN0 C_ NN0*
2		0nn0 9310	. 2 |- 0 e. NN0
3	1, 2	sselii 3190	1 |- 0 e. NN0*

Syntax hints:   e. wcel 2176   0cc0 7925   NN0cn0 9295  NN0*cxnn0 9358

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-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  ax-1cn 8018  ax-icn 8020  ax-addcl 8021  ax-mulcl 8023  ax-i2m1 8030

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-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-n0 9296  df-xnn0 9359

This theorem is referenced by:  0tonninf  10585