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Theorem bj-vtoclgf 11018
Description: Weakening two hypotheses of vtoclgf 2668. (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 11017 . 2 (∀𝑥(𝑥 = 𝐴 → (𝜑𝜓)) → (𝐴𝑉𝜓))
5 bj-vtoclgf.maj . 2 (𝑥 = 𝐴 → (𝜑𝜓))
64, 5mpg 1381 1 (𝐴𝑉𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  wnf 1390  wcel 1434  wnfc 2210
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614
This theorem is referenced by:  elabgf2  11022
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