Theorem pm2.61danel

Description: Deduction eliminating an elementhood in an antecedent. (Contributed by AV, 5-Dec-2021)

	Ref	Expression
Hypotheses	pm2.61danel.1	|- ( ( ph /\ A e. B ) -> ps )
	pm2.61danel.2	|- ( ( ph /\ A e/ B ) -> ps )
Assertion	pm2.61danel	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		pm2.61danel.1	|- ( ( ph /\ A e. B ) -> ps )
2		pm2.61danel.2	|- ( ( ph /\ A e/ B ) -> ps )
3		df-nel	|- ( A e/ B <-> -. A e. B )
4	3 2	sylan2br	|- ( ( ph /\ -. A e. B ) -> ps )
5	1 4	pm2.61dan	|- ( ph -> ps )