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Theorem moexex 2349
 Description: "At most one" double quantification. (Contributed by NM, 3-Dec-2001.)
Hypothesis
Ref Expression
moexex.1
Assertion
Ref Expression
moexex

Proof of Theorem moexex
StepHypRef Expression
1 nfmo1 2291 . . . . 5
2 nfa1 1806 . . . . . 6
3 nfe1 1747 . . . . . . 7
43nfmo 2297 . . . . . 6
52, 4nfim 1832 . . . . 5
61, 5nfim 1832 . . . 4
7 moexex.1 . . . . . 6
87nfmo 2297 . . . . . 6
9 mopick 2342 . . . . . . . 8
109ex 424 . . . . . . 7
1110com3r 75 . . . . . 6
127, 8, 11alrimd 1785 . . . . 5
13 moim 2326 . . . . . 6
1413spsd 1771 . . . . 5
1512, 14syl6 31 . . . 4
166, 15exlimi 1821 . . 3
177nfex 1865 . . . . . . . 8
18 exsimpl 1602 . . . . . . . 8
1917, 18exlimi 1821 . . . . . . 7
2019con3i 129 . . . . . 6
21 exmo 2325 . . . . . . 7
2221ori 365 . . . . . 6
2320, 22syl 16 . . . . 5
2423a1d 23 . . . 4
2524a1d 23 . . 3
2616, 25pm2.61i 158 . 2
2726imp 419 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550  wnf 1553  wmo 2281 This theorem is referenced by:  moexexv  2350  2moswap  2355 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
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