Theorem abanssl 4270

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	⊢ {𝑥 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑥 ∣ 𝜑}

Proof of Theorem abanssl

Step	Hyp	Ref	Expression
1		simpl 487	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	ss2abi 4026	1 ⊢ {𝑥 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑥 ∣ 𝜑}

Syntax hints:   ∧ wa 400  {cab 2747   ⊆ wss 3911

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-sb 2098  df-clab 2748  df-ss 3928

This theorem is referenced by:  f1setex  8854  isghm  19286  sn-isghm  43332  fsetprcnexALT  47723