Theorem abanssl

Description: A class abstraction with a conjunction is a subset of the class abstraction with the left conjunct only. (Contributed by AV, 7-Aug-2024) (Proof shortened by SN, 22-Aug-2024)

	Ref	Expression
Assertion	abanssl	$$⊢\left\{f|\left(\phi \wedge \psi \right)\right\}\subseteq \left\{f|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(\phi \wedge \psi \right)\to \phi$$
2	1	ss2abi	$$⊢\left\{f|\left(\phi \wedge \psi \right)\right\}\subseteq \left\{f|\phi \right\}$$