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Theorem ss2abdvOLD 3999
Description: Obsolete version of ss2abdv 3997 as of 28-Jun-2024. (Contributed by NM, 29-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ss2abdvOLD.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
ss2abdvOLD (𝜑 → {𝑥𝜓} ⊆ {𝑥𝜒})
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem ss2abdvOLD
StepHypRef Expression
1 ss2abdvOLD.1 . . 3 (𝜑 → (𝜓𝜒))
21alrimiv 1930 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 ss2ab 3993 . 2 ({𝑥𝜓} ⊆ {𝑥𝜒} ↔ ∀𝑥(𝜓𝜒))
42, 3sylibr 233 1 (𝜑 → {𝑥𝜓} ⊆ {𝑥𝜒})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1537  {cab 2715  wss 3887
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-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2889  df-v 3434  df-in 3894  df-ss 3904
This theorem is referenced by: (None)
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