Theorem abanssl 4242

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 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	ss2abi 4000	1 ⊢ {𝑓 ∣ (𝜑 ∧ 𝜓)} ⊆ {𝑓 ∣ 𝜑}

Syntax hints:   ∧ wa 397  {cab 2719   ⊆ wss 3885

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016

This theorem depends on definitions:  df-bi 209  df-an 398  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-ss 3902

This theorem is referenced by:  f1setex  8798  isghm  19185  sn-isghm  43138  fsetprcnexALT  47539