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Theorem moexex 2390
 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 2330 . . . 4
2 nfa1 1999 . . . . 5
3 nfe1 1935 . . . . . 6
43nfmo 2336 . . . . 5
52, 4nfim 2023 . . . 4
6 moexex.1 . . . . . . 7
76nfmo 2336 . . . . . 6
8 mopick 2384 . . . . . . . 8
98ex 441 . . . . . . 7
109com23 80 . . . . . 6
117, 6, 10alrimd 1979 . . . . 5
12 moim 2368 . . . . . 6
1312spsd 1965 . . . . 5
1411, 13syl6 33 . . . 4
151, 5, 14exlimd 2017 . . 3
166nfex 2050 . . . . . . 7
17 exsimpl 1737 . . . . . . 7
1816, 17exlimi 2015 . . . . . 6
19 exmo 2344 . . . . . . 7
2019ori 382 . . . . . 6
2118, 20nsyl4 149 . . . . 5
2221con1i 134 . . . 4
2322a1d 25 . . 3
2415, 23pm2.61d1 164 . 2
2524imp 436 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 376  wal 1450  wex 1671  wnf 1675  wmo 2320 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-eu 2323  df-mo 2324 This theorem is referenced by:  moexexv  2391  2moswap  2396
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