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Theorem vtocldOLD 3510
Description: Obsolete version of vtocld 3509 as of 2-Sep-2024. (Contributed by Mario Carneiro, 15-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
vtocld.1 (𝜑𝐴𝑉)
vtocld.2 ((𝜑𝑥 = 𝐴) → (𝜓𝜒))
vtocld.3 (𝜑𝜓)
Assertion
Ref Expression
vtocldOLD (𝜑𝜒)
Distinct variable groups:   𝑥,𝐴   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝑉(𝑥)

Proof of Theorem vtocldOLD
StepHypRef Expression
1 vtocld.1 . 2 (𝜑𝐴𝑉)
2 vtocld.2 . 2 ((𝜑𝑥 = 𝐴) → (𝜓𝜒))
3 vtocld.3 . 2 (𝜑𝜓)
4 nfv 1917 . 2 𝑥𝜑
5 nfcvd 2906 . 2 (𝜑𝑥𝐴)
6 nfvd 1918 . 2 (𝜑 → Ⅎ𝑥𝜒)
71, 2, 3, 4, 5, 6vtocldf 3508 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396   = wceq 1541  wcel 2106
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  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 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-ex 1782  df-nf 1786  df-cleq 2728  df-clel 2814  df-nfc 2887
This theorem is referenced by: (None)
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