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Theorem 19.27v 1905
Description: Version of 19.27 2093 with a dv condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004.)
Assertion
Ref Expression
19.27v (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.27v
StepHypRef Expression
1 19.26 1795 . 2 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2 19.3v 1894 . . 3 (∀𝑥𝜓𝜓)
32anbi2i 729 . 2 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) ↔ (∀𝑥𝜑𝜓))
41, 3bitri 264 1 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
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  ax-5 1836  ax-6 1885
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by:  rexrsb  40503
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