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Theorem spsbimvOLD 2251
 Description: Obsolete version of spsbim 2023 as of 6-Jul-2023. Specialization of implication. Version of spsbim 2023 with a disjoint variable condition, not requiring ax-13 2301. (Contributed by Wolf Lammen, 19-Jan-2023.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
spsbimvOLD (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓))
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑥,𝑦)

Proof of Theorem spsbimvOLD
StepHypRef Expression
1 nfa1 2088 . 2 𝑥𝑥(𝜑𝜓)
2 sp 2111 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2sbimd 2172 1 (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1505  [wsb 2015 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-10 2079  ax-12 2106 This theorem depends on definitions:  df-bi 199  df-or 834  df-ex 1743  df-nf 1747  df-sb 2016 This theorem is referenced by: (None)
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