Theorem ssidOLD 2635

Description: Any class is a subclass of itself. Exercise 10 of [TakeutiZaring] p. 18.

Assertion

Ref	Expression
ssidOLD	|- A C_ A

Proof of Theorem ssidOLD

Step	Hyp	Ref	Expression
1		eqid 1884	. . 3 |- A = A
2		eqss 2631	. . 3 |- (A = A <-> (A C_ A /\ A C_ A))
3	1, 2	mpbi 206	. 2 |- (A C_ A /\ A C_ A)
4	3	simpli 347	1 |- A C_ A

Syntax hints:   /\ wa 240   = wceq 1298   C_ wss 2593

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-in 2603  df-ss 2605

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