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Theorem bj-sbime 14765
Description: A strengthening of sbie 1801 (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 1529 . 2 (𝜓 → ∀𝑥𝜓)
3 bj-sbime.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-sbimeh 14764 1 ([𝑦 / 𝑥]𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1470  [wsb 1772
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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773
This theorem is referenced by:  setindis  14959  bdsetindis  14961
  Copyright terms: Public domain W3C validator