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Database SUPPLEMENTARY MATERIAL (USERS' MATHBOXES) Mathbox for BJ First-order logic Removing dependencies on ax-13 (and ax-11) bj-cbv3hv2
Description: Version of cbv3h with two disjoint variable conditions, which does not
require ax-11 nor ax-13 . (Contributed by BJ , 24-Jun-2019)
(Proof modification is discouraged.)
Ref
Expression
Hypotheses
bj-cbv3hv2.nf ⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
bj-cbv3hv2.1 ⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
Assertion
bj-cbv3hv2 ⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑦 𝜓 )
Proof
Step
Hyp
Ref
Expression
1
bj-cbv3hv2.nf ⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
2
bj-cbv3hv2.1 ⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
3
1
nf5i ⊢ Ⅎ 𝑥 𝜓
4
3 2
cbv3v2 ⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑦 𝜓 )