Theorem unisn0 39222

Description: The union of the singleton of the empty set is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020.)

Assertion

Ref	Expression
unisn0	|- U. { (/) } = (/)

Proof of Theorem unisn0

Step	Hyp	Ref	Expression
1		ssid 3624	. 2 |- { (/) } C_ { (/) }
2		uni0b 4463	. 2 |- ( U. { (/) } = (/) <-> { (/) } C_ { (/) } )
3	1, 2	mpbir 221	1 |- U. { (/) } = (/)

Syntax hints:   = wceq 1483   C_ wss 3574   (/)c0 3915   {csn 4177   U.cuni 4436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-v 3202  df-dif 3577  df-in 3581  df-ss 3588  df-nul 3916  df-sn 4178  df-uni 4437

This theorem is referenced by:  founiiun0  39377