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Theorem bj-vtoclgft 9183
Description: Weakening two hypotheses of vtoclgf 2606. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
bj-vtoclgf.nf1 xA
bj-vtoclgf.nf2 xψ
bj-vtoclgf.min (x = Aφ)
Assertion
Ref Expression
bj-vtoclgft (x(x = A → (φψ)) → (A 𝑉ψ))

Proof of Theorem bj-vtoclgft
StepHypRef Expression
1 elex 2560 . 2 (A 𝑉A V)
2 bj-vtoclgf.nf1 . . . 4 xA
32issetf 2556 . . 3 (A V ↔ x x = A)
4 bj-vtoclgf.nf2 . . . 4 xψ
5 bj-vtoclgf.min . . . 4 (x = Aφ)
64, 5bj-exlimmp 9178 . . 3 (x(x = A → (φψ)) → (x x = Aψ))
73, 6syl5bi 141 . 2 (x(x = A → (φψ)) → (A V → ψ))
81, 7syl5 28 1 (x(x = A → (φψ)) → (A 𝑉ψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240   = wceq 1242  wnf 1346  wex 1378   wcel 1390  wnfc 2162  Vcvv 2551
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553
This theorem is referenced by:  bj-vtoclgf  9184  elabgft1  9186  bj-rspgt  9194
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