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Theorem 19.28v 1989
Description: Version of 19.28 2227 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
19.28v (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.28v
StepHypRef Expression
1 19.26 1869 . 2 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2 19.3v 1980 . 2 (∀𝑥𝜑𝜑)
31, 2bianbi 627 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395  wal 1537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779
This theorem is referenced by:  reu6  3731  dfer2  8747  kmlem14  10205  kmlem15  10206  bnj1176  35020  bnj1186  35022  ismnuprim  44318  19.28vv  44410
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