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Theorem 19.26-2 1863
Description: Theorem 19.26 1862 with two quantifiers. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
19.26-2 (∀𝑥𝑦(𝜑𝜓) ↔ (∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓))

Proof of Theorem 19.26-2
StepHypRef Expression
1 19.26 1862 . . 3 (∀𝑦(𝜑𝜓) ↔ (∀𝑦𝜑 ∧ ∀𝑦𝜓))
21albii 1811 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(∀𝑦𝜑 ∧ ∀𝑦𝜓))
3 19.26 1862 . 2 (∀𝑥(∀𝑦𝜑 ∧ ∀𝑦𝜓) ↔ (∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓))
42, 3bitri 276 1 (∀𝑥𝑦(𝜑𝜓) ↔ (∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801
This theorem depends on definitions:  df-bi 208  df-an 397
This theorem is referenced by:  2mo2  2725  opelopabt  5410  fun11  6421  dford4  39504  undmrnresiss  39842  ichan  43507
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