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Theorem ssrab2OLD 4013
Description: Obsolete version of ssrab2 4012 as of 8-Aug-2024. (Contributed by NM, 19-Mar-1997.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
ssrab2OLD {𝑥𝐴𝜑} ⊆ 𝐴
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem ssrab2OLD
StepHypRef Expression
1 df-rab 3073 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
2 ssab2 4011 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
31, 2eqsstri 3954 1 {𝑥𝐴𝜑} ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 396  wcel 2106  {cab 2715  {crab 3068  wss 3886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3431  df-in 3893  df-ss 3903
This theorem is referenced by: (None)
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