Theorem abanssl 4256

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 3991	1 ⊢ {𝑥 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑥 ∣ 𝜑}

This proof depends on syntax axioms:   ∧ wa 401  {cab 2738   ⊆ wss 3895

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-ss 3896

This theorem is used by:  f1setex  8879  isghm  19430  sn-isghm  43685  fsetprcnexALT  48132