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Theorem bj-vtoclgf 9915
 Description: Weakening two hypotheses of vtoclgf 2612. (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 9914 . 2 (∀𝑥(𝑥 = 𝐴 → (𝜑𝜓)) → (𝐴𝑉𝜓))
5 bj-vtoclgf.maj . 2 (𝑥 = 𝐴 → (𝜑𝜓))
64, 5mpg 1340 1 (𝐴𝑉𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243  Ⅎwnf 1349   ∈ wcel 1393  Ⅎwnfc 2165 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559 This theorem is referenced by:  elabgf2  9919
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