Theorem abanssl 4330

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.)

Assertion

Ref	Expression
abanssl	⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜑}

Proof of Theorem abanssl

Step	Hyp	Ref	Expression
1		simpl 482	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	ss2abi 4090	1 ⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜑}

Syntax hints:   ∧ wa 395  {cab 2717   ⊆ wss 3976

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-sb 2065  df-clab 2718  df-ss 3993

This theorem is referenced by:  f1setex  8915  isghm  19255  sn-isghm  42628  fsetprcnexALT  46977