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Theorem spcegft 2626
 Description: A closed version of spcegf 2630. (Contributed by Jim Kingdon, 22-Jun-2018.)
Hypotheses
Ref Expression
spcimgft.1 xψ
spcimgft.2 xA
Assertion
Ref Expression
spcegft (x(x = A → (φψ)) → (A B → (ψxφ)))

Proof of Theorem spcegft
StepHypRef Expression
1 bi2 121 . . . 4 ((φψ) → (ψφ))
21imim2i 12 . . 3 ((x = A → (φψ)) → (x = A → (ψφ)))
32alimi 1341 . 2 (x(x = A → (φψ)) → x(x = A → (ψφ)))
4 spcimgft.1 . . 3 xψ
5 spcimgft.2 . . 3 xA
64, 5spcimegft 2625 . 2 (x(x = A → (ψφ)) → (A B → (ψxφ)))
73, 6syl 14 1 (x(x = A → (φψ)) → (A B → (ψxφ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240   = wceq 1242  Ⅎwnf 1346  ∃wex 1378   ∈ wcel 1390  Ⅎwnfc 2162 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-bndl 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:  spcegf  2630
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