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Theorem 2moex 2697
Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 2122 . . 3 𝑦𝑦𝜑
21nfmo 2604 . 2 𝑦∃*𝑥𝑦𝜑
3 19.8a 2146 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2583 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimi 2180 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1523  wex 1765  ∃*wmo 2576
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996  ax-10 2114  ax-11 2128  ax-12 2143  ax-13 2346
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1528  df-ex 1766  df-nf 1770  df-mo 2578
This theorem is referenced by:  2eu2  2710  2eu5OLD  2715
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