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Theorem vtoclALT 3246
 Description: Alternate proof of vtocl 3245. Shorter but requires more axioms. (Contributed by NM, 30-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
vtocl.1 𝐴 ∈ V
vtocl.2 (𝑥 = 𝐴 → (𝜑𝜓))
vtocl.3 𝜑
Assertion
Ref Expression
vtoclALT 𝜓
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem vtoclALT
StepHypRef Expression
1 nfv 1840 . 2 𝑥𝜓
2 vtocl.1 . 2 𝐴 ∈ V
3 vtocl.2 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
4 vtocl.3 . 2 𝜑
51, 2, 3, 4vtoclf 3244 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   = wceq 1480   ∈ wcel 1987  Vcvv 3186 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-12 2044  ax-ext 2601 This theorem depends on definitions:  df-bi 197  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-v 3188 This theorem is referenced by: (None)
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