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Theorem 19.44v 1909
Description: Version of 19.44 2104 with a dv condition, requiring fewer axioms. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
19.44v (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.44v
StepHypRef Expression
1 19.43 1807 . 2 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓))
2 19.9v 1893 . . 3 (∃𝑥𝜓𝜓)
32orbi2i 541 . 2 ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ (∃𝑥𝜑𝜓))
41, 3bitri 264 1 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 383  wex 1701
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-or 385  df-ex 1702
This theorem is referenced by:  grothprim  9616
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