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Theorem bj-sbime 14922
Description: A strengthening of sbie 1802 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbime.nf 𝑥𝜓
bj-sbime.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-sbime ([𝑦 / 𝑥]𝜑𝜓)

Proof of Theorem bj-sbime
StepHypRef Expression
1 bj-sbime.nf . . 3 𝑥𝜓
21nfri 1530 . 2 (𝜓 → ∀𝑥𝜓)
3 bj-sbime.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-sbimeh 14921 1 ([𝑦 / 𝑥]𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1471  [wsb 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774
This theorem is referenced by:  setindis  15116  bdsetindis  15118
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