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Theorem 19.29r2 1554
Description: Variation of Theorem 19.29 of [Margaris] p. 90 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 1553 . 2 ((∃𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∃𝑥(∃𝑦𝜑 ∧ ∀𝑦𝜓))
2 19.29r 1553 . . 3 ((∃𝑦𝜑 ∧ ∀𝑦𝜓) → ∃𝑦(𝜑𝜓))
32eximi 1532 . 2 (∃𝑥(∃𝑦𝜑 ∧ ∀𝑦𝜓) → ∃𝑥𝑦(𝜑𝜓))
41, 3syl 14 1 ((∃𝑥𝑦𝜑 ∧ ∀𝑥𝑦𝜓) → ∃𝑥𝑦(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wal 1283  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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