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Theorem moexex 2363
 Description: "At most one" double quantification. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Wolf Lammen, 28-Dec-2018.)
Hypothesis
Ref Expression
moexex.1
Assertion
Ref Expression
moexex

Proof of Theorem moexex
StepHypRef Expression
1 nfmo1 2295 . . . 4
2 nfa1 1897 . . . . 5
3 nfe1 1840 . . . . . 6
43nfmo 2301 . . . . 5
52, 4nfim 1920 . . . 4
6 moexex.1 . . . . . . 7
76nfmo 2301 . . . . . 6
8 mopick 2356 . . . . . . . 8
98ex 434 . . . . . . 7
109com23 78 . . . . . 6
117, 6, 10alrimd 1881 . . . . 5
12 moim 2339 . . . . . 6
1312spsd 1867 . . . . 5
1411, 13syl6 33 . . . 4
151, 5, 14exlimd 1914 . . 3
166nfex 1948 . . . . . . 7
17 exsimpl 1677 . . . . . . 7
1816, 17exlimi 1912 . . . . . 6
19 exmo 2309 . . . . . . 7
2019ori 375 . . . . . 6
2118, 20nsyl4 142 . . . . 5
2221con1i 129 . . . 4
2322a1d 25 . . 3
2415, 23pm2.61d1 159 . 2
2524imp 429 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  E*wmo 2283 This theorem is referenced by:  moexexv  2364  2moswap  2369 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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