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Theorem snsslVD 38582
Description: Virtual deduction proof of snssl 38583. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
snsslVD.1 𝐴 ∈ V
Assertion
Ref Expression
snsslVD ({𝐴} ⊆ 𝐵𝐴𝐵)

Proof of Theorem snsslVD
StepHypRef Expression
1 idn1 38307 . . 3 (   {𝐴} ⊆ 𝐵   ▶   {𝐴} ⊆ 𝐵   )
2 snsslVD.1 . . . 4 𝐴 ∈ V
32snid 4184 . . 3 𝐴 ∈ {𝐴}
4 ssel2 3582 . . 3 (({𝐴} ⊆ 𝐵𝐴 ∈ {𝐴}) → 𝐴𝐵)
51, 3, 4e10an 38437 . 2 (   {𝐴} ⊆ 𝐵   ▶   𝐴𝐵   )
65in1 38304 1 ({𝐴} ⊆ 𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1987  Vcvv 3189  wss 3559  {csn 4153
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3191  df-in 3566  df-ss 3573  df-sn 4154  df-vd1 38303
This theorem is referenced by: (None)
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