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Metamath Proof Explorer

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	⊢ { 𝑓 ∣ ( 𝜑 ∧ 𝜓 ) } ⊆ { 𝑓 ∣ 𝜑 }

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
2	1	ss2abi	⊢ { 𝑓 ∣ ( 𝜑 ∧ 𝜓 ) } ⊆ { 𝑓 ∣ 𝜑 }