Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-vtoclgf GIF version

Theorem bj-vtoclgf 11106
Description: Weakening two hypotheses of vtoclgf 2671. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
bj-vtoclgf.nf1 𝑥𝐴
bj-vtoclgf.nf2 𝑥𝜓
bj-vtoclgf.min (𝑥 = 𝐴𝜑)
bj-vtoclgf.maj (𝑥 = 𝐴 → (𝜑𝜓))
Assertion
Ref Expression
bj-vtoclgf (𝐴𝑉𝜓)

Proof of Theorem bj-vtoclgf
StepHypRef Expression
1 bj-vtoclgf.nf1 . . 3 𝑥𝐴
2 bj-vtoclgf.nf2 . . 3 𝑥𝜓
3 bj-vtoclgf.min . . 3 (𝑥 = 𝐴𝜑)
41, 2, 3bj-vtoclgft 11105 . 2 (∀𝑥(𝑥 = 𝐴 → (𝜑𝜓)) → (𝐴𝑉𝜓))
5 bj-vtoclgf.maj . 2 (𝑥 = 𝐴 → (𝜑𝜓))
64, 5mpg 1383 1 (𝐴𝑉𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wnf 1392  wcel 1436  wnfc 2212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617
This theorem is referenced by:  elabgf2  11110
  Copyright terms: Public domain W3C validator