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Theorem vtoclgOLD 3554
 Description: Obsolete version of vtoclg 3553 as of 20-Apr-2024. (Contributed by NM, 17-Apr-1995.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
vtoclgOLD.1 (𝑥 = 𝐴 → (𝜑𝜓))
vtoclgOLD.2 𝜑
Assertion
Ref Expression
vtoclgOLD (𝐴𝑉𝜓)
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝑉(𝑥)

Proof of Theorem vtoclgOLD
StepHypRef Expression
1 nfv 1916 . 2 𝑥𝜓
2 vtoclgOLD.1 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
3 vtoclgOLD.2 . 2 𝜑
41, 2, 3vtoclg1f 3552 1 (𝐴𝑉𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   = wceq 1538   ∈ wcel 2115 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-cleq 2817  df-clel 2896 This theorem is referenced by: (None)
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