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Theorem bj-sbime 10735
Description: A strengthening of sbie 1715 (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 1453 . 2 (𝜓 → ∀𝑥𝜓)
3 bj-sbime.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-sbimeh 10734 1 ([𝑦 / 𝑥]𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1390  [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687
This theorem is referenced by:  setindis  10920  bdsetindis  10922
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