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Theorem abanssr 4242
Description: A class abstraction with a conjunction is a subset of the class abstraction with the right conjunct only. (Contributed by AV, 7-Aug-2024.) (Proof shortened by SN, 22-Aug-2024.)
Assertion
Ref Expression
abanssr {𝑓 ∣ (𝜑𝜓)} ⊆ {𝑓𝜓}

Proof of Theorem abanssr
StepHypRef Expression
1 simpr 485 . 2 ((𝜑𝜓) → 𝜓)
21ss2abi 4005 1 {𝑓 ∣ (𝜑𝜓)} ⊆ {𝑓𝜓}
Colors of variables: wff setvar class
Syntax hints:  wa 396  {cab 2717  wss 3892
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-in 3899  df-ss 3909
This theorem is referenced by:  hashf1lem1  14158
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