This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Database ZF (ZERMELO-FRAENKEL) SET THEORY ZF Set Theory - start with the Axiom of Extensionality Restricted quantification Restricted universal and existential quantification ralimdvvOLD
Description: Obsolete version of ralimdvv as of 18-Nov-2025. (Contributed by Scott
Fenton , 2-Mar-2025) (New usage is discouraged.)
(Proof modification is discouraged.)
Ref
Expression
Hypothesis
ralimdvvOLD.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion
ralimdvvOLD ⊢ ( 𝜑 → ( ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜓 → ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜒 ) )
Proof
Step
Hyp
Ref
Expression
1
ralimdvvOLD.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2
1
adantr ⊢ ( ( 𝜑 ∧ ( 𝑥 ∈ 𝐴 ∧ 𝑦 ∈ 𝐵 ) ) → ( 𝜓 → 𝜒 ) )
3
2
ralimdvva ⊢ ( 𝜑 → ( ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜓 → ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜒 ) )