MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  vtocldOLD Structured version   Visualization version   GIF version

Theorem vtocldOLD 3504
Description: Obsolete version of vtocld 3503 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 1916 . 2 𝑥𝜑
5 nfcvd 2905 . 2 (𝜑𝑥𝐴)
6 nfvd 1917 . 2 (𝜑 → Ⅎ𝑥𝜒)
71, 2, 3, 4, 5, 6vtocldf 3502 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396   = wceq 1540  wcel 2105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2886
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator