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

Theorem vtoclgOLDOLD 3529
Description: Obsolete version of vtoclg 3527 as of 20-Apr-2024. (Contributed by NM, 17-Apr-1995.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
vtoclg.1 (𝑥 = 𝐴 → (𝜑𝜓))
vtoclg.2 𝜑
Assertion
Ref Expression
vtoclgOLDOLD (𝐴𝑉𝜓)
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝑉(𝑥)

Proof of Theorem vtoclgOLDOLD
StepHypRef Expression
1 nfv 1918 . 2 𝑥𝜓
2 vtoclg.1 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
3 vtoclg.2 . 2 𝜑
41, 2, 3vtoclg1f 3526 1 (𝐴𝑉𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wcel 2107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-clel 2811
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator