Theorem dfss1OLD 3818

Description: Obsolete as of 22-Jul-2021. (Contributed by NM, 10-Jan-2015.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
dfss1OLD	|- ( A C_ B <-> ( B i^i A ) = A )

Proof of Theorem dfss1OLD

Step	Hyp	Ref	Expression
1		df-ss 3588	. 2 |- ( A C_ B <-> ( A i^i B ) = A )
2		incom 3805	. . 3 |- ( A i^i B ) = ( B i^i A )
3	2	eqeq1i 2627	. 2 |- ( ( A i^i B ) = A <-> ( B i^i A ) = A )
4	1, 3	bitri 264	1 |- ( A C_ B <-> ( B i^i A ) = A )

Syntax hints:   <-> wb 196   = wceq 1483   i^i cin 3573   C_ wss 3574

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-v 3202  df-in 3581  df-ss 3588

This theorem is referenced by: (None)