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Theorem 19.28v 1987
Description: Version of 19.28 2217 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 1866 . 2 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2 19.3v 1978 . 2 (∀𝑥𝜑𝜑)
31, 2bianbi 625 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 394  wal 1532
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1775
This theorem is referenced by:  reu6  3720  dfer2  8735  kmlem14  10206  kmlem15  10207  bnj1176  34850  bnj1186  34852  ismnuprim  43968  19.28vv  44060
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