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Theorem 19.29r2 1843
Description: Variation of 19.29r 1842 with double quantification. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
19.29r2 ((∃𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∃𝑥𝑦(𝜑𝜓))

Proof of Theorem 19.29r2
StepHypRef Expression
1 19.29r 1842 . 2 ((∃𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∃𝑥(∃𝑦𝜑 ∧ ∀𝑦𝜓))
2 19.29r 1842 . . 3 ((∃𝑦𝜑 ∧ ∀𝑦𝜓) → ∃𝑦(𝜑𝜓))
32eximi 1802 . 2 (∃𝑥(∃𝑦𝜑 ∧ ∀𝑦𝜓) → ∃𝑥𝑦(𝜑𝜓))
41, 3syl 17 1 ((∃𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∃𝑥𝑦(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1521  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by: (None)
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