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Theorem 3ralbii 34338
Description: Inference adding three restricted universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 25-Jul-2019.)
Hypothesis
Ref Expression
3ralbii.1 (𝜑𝜓)
Assertion
Ref Expression
3ralbii (∀𝑥𝐴𝑦𝐵𝑧𝐶 𝜑 ↔ ∀𝑥𝐴𝑦𝐵𝑧𝐶 𝜓)

Proof of Theorem 3ralbii
StepHypRef Expression
1 3ralbii.1 . . 3 (𝜑𝜓)
212ralbii 3119 . 2 (∀𝑦𝐵𝑧𝐶 𝜑 ↔ ∀𝑦𝐵𝑧𝐶 𝜓)
32ralbii 3118 1 (∀𝑥𝐴𝑦𝐵𝑧𝐶 𝜑 ↔ ∀𝑥𝐴𝑦𝐵𝑧𝐶 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wral 3050
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-ral 3055
This theorem is referenced by: (None)
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