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Theorem ss2abdvOLD 4057
Description: Obsolete version of ss2abdv 4055 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 1922 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 ss2ab 4051 . 2 ({𝑥𝜓} ⊆ {𝑥𝜒} ↔ ∀𝑥(𝜓𝜒))
42, 3sylibr 233 1 (𝜑 → {𝑥𝜓} ⊆ {𝑥𝜒})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  {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-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-nfc 2879  df-v 3470  df-in 3950  df-ss 3960
This theorem is referenced by: (None)
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