Theorem ssctOLD

Description: Obsolete version of ssct as of 7-Dec-2024. (Contributed by Thierry Arnoux, 31-Jan-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	ssctOLD	|- ( ( A C_ B /\ B ~<_ _om ) -> A ~<_ _om )

Proof

Step	Hyp	Ref	Expression
1		ctex	|- ( B ~<_ _om -> B e. _V )
2		ssdomg	|- ( B e. _V -> ( A C_ B -> A ~<_ B ) )
3	1 2	syl	|- ( B ~<_ _om -> ( A C_ B -> A ~<_ B ) )
4	3	impcom	|- ( ( A C_ B /\ B ~<_ _om ) -> A ~<_ B )
5		domtr	|- ( ( A ~<_ B /\ B ~<_ _om ) -> A ~<_ _om )
6	4 5	sylancom	|- ( ( A C_ B /\ B ~<_ _om ) -> A ~<_ _om )