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Theorem sb4vOLD 2093
 Description: Obsolete as of 30-Jul-2023. Use sb6 2090 instead. (Contributed by BJ, 23-Jun-2019.) (Proof shortened by Steven Nguyen, 8-Jul-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sb4vOLD ([𝑦 / 𝑥]𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem sb4vOLD
StepHypRef Expression
1 sb6 2090 . 2 ([𝑦 / 𝑥]𝜑 ↔ ∀𝑥(𝑥 = 𝑦𝜑))
21biimpi 219 1 ([𝑦 / 𝑥]𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  [wsb 2069 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070 This theorem is referenced by:  sbi1vOLD  2317
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