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Theorem 19.44v 1997
Description: Version of 19.44 2231 with a disjoint variable 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 1886 . 2 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓))
2 19.9v 1988 . . 3 (∃𝑥𝜓𝜓)
32orbi2i 912 . 2 ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ (∃𝑥𝜑𝜓))
41, 3bitri 275 1 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wo 846  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972
This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783
This theorem is referenced by:  grothprim  10829
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