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Theorem bj-vtoclgf 7022
Description: Weakening two hypotheses of vtoclgf 2589. (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 (A 𝑉ψ)

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 7021 . 2 (x(x = A → (φψ)) → (A 𝑉ψ))
5 bj-vtoclgf.maj . 2 (x = A → (φψ))
64, 5mpg 1320 1 (A 𝑉ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228  wnf 1329   wcel 1374  wnfc 2147
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537
This theorem is referenced by:  elabgf2  7026
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