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Database ZF (ZERMELO-FRAENKEL) SET THEORY ZF Set Theory - start with the Axiom of Extensionality Restricted quantification Restricted universal and existential quantification ralimd4vOLD
Description: Obsolete version of ralimd4v as of 18-Nov-2025. (Contributed by Scott
Fenton , 2-Mar-2025) (New usage is discouraged.)
(Proof modification is discouraged.)
Ref
Expression
Hypothesis
ralimd4vOLD.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion
ralimd4vOLD ⊢ ( 𝜑 → ( ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜓 → ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜒 ) )
Proof
Step
Hyp
Ref
Expression
1
ralimd4vOLD.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2
1
ralimdvvOLD ⊢ ( 𝜑 → ( ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜓 → ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜒 ) )
3
2
ralimdvvOLD ⊢ ( 𝜑 → ( ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜓 → ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 ∀ 𝑧 ∈ 𝐶 ∀ 𝑤 ∈ 𝐷 𝜒 ) )