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Theorem bj-vtoclgft 7021
 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)
Assertion
Ref Expression
bj-vtoclgft (x(x = A → (φψ)) → (A 𝑉ψ))

Proof of Theorem bj-vtoclgft
StepHypRef Expression
1 elex 2543 . 2 (A 𝑉A V)
2 bj-vtoclgf.nf1 . . . 4 xA
32issetf 2540 . . 3 (A V ↔ x x = A)
4 bj-vtoclgf.nf2 . . . 4 xψ
5 bj-vtoclgf.min . . . 4 (x = Aφ)
64, 5bj-exlimmp 7016 . . 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 1226   = wceq 1228  Ⅎwnf 1329  ∃wex 1362   ∈ wcel 1374  Ⅎwnfc 2147  Vcvv 2535 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:  bj-vtoclgf  7022  elabgft1  7024  bj-rspgt  7032
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