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Theorem abanssl 4296
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 ∣ (𝜑𝜓)} ⊆ {𝑓𝜑}

Proof of Theorem abanssl
StepHypRef Expression
1 simpl 482 . 2 ((𝜑𝜓) → 𝜑)
21ss2abi 4058 1 {𝑓 ∣ (𝜑𝜓)} ⊆ {𝑓𝜑}
Colors of variables: wff setvar class
Syntax hints:  wa 395  {cab 2703  wss 3943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-in 3950  df-ss 3960
This theorem is referenced by:  f1setex  8850  fsetprcnexALT  46325
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