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Theorem 19.26-2 1796
Description: Theorem 19.26 1795 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 1795 . . 3 (∀𝑦(𝜑𝜓) ↔ (∀𝑦𝜑 ∧ ∀𝑦𝜓))
21albii 1744 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(∀𝑦𝜑 ∧ ∀𝑦𝜓))
3 19.26 1795 . 2 (∀𝑥(∀𝑦𝜑 ∧ ∀𝑦𝜓) ↔ (∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓))
42, 3bitri 264 1 (∀𝑥𝑦(𝜑𝜓) ↔ (∀𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-an 386
This theorem is referenced by:  2mo2  2549  opelopabt  4947  fun11  5921  dford4  37073  undmrnresiss  37388
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