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Theorem moexex 2273
 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 2215 . . . . 5
2 nfa1 1788 . . . . . 6
3 nfe1 1732 . . . . . . 7
43nfmo 2221 . . . . . 6
52, 4nfim 1813 . . . . 5
61, 5nfim 1813 . . . 4
7 moexex.1 . . . . . 6
87nfmo 2221 . . . . . 6
9 mopick 2266 . . . . . . . 8
109ex 423 . . . . . . 7
1110com3r 73 . . . . . 6
127, 8, 11alrimd 1769 . . . . 5
13 moim 2250 . . . . . 6
1413spsd 1755 . . . . 5
1512, 14syl6 29 . . . 4
166, 15exlimi 1803 . . 3
177nfex 1843 . . . . . . . 8
18 exsimpl 1592 . . . . . . . 8
1917, 18exlimi 1803 . . . . . . 7
2019con3i 127 . . . . . 6
21 exmo 2249 . . . . . . 7
2221ori 364 . . . . . 6
2320, 22syl 15 . . . . 5
2423a1d 22 . . . 4
2524a1d 22 . . 3
2616, 25pm2.61i 156 . 2
2726imp 418 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541  wnf 1544  wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  moexexv  2274  2moswap  2279
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