Theorem abanssl 4207

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 486	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	ss2abi 3973	1 ⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜑}

Syntax hints:   ∧ wa 399  {cab 2735   ⊆ wss 3860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2121  ax-ext 2729

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-in 3867  df-ss 3877

This theorem is referenced by:  f1setex  8452  fsetprcnexALT  44064