Theorem abanssl 4260

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 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	ss2abi 4017	1 ⊢ {𝑥 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑥 ∣ 𝜑}

This proof depends on syntax axioms:   ∧ wa 401  {cab 2740   ⊆ wss 3902

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-ss 3919

This theorem is used by:  f1setex  8861  isghm  19344  sn-isghm  43506  fsetprcnexALT  47937