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Theorem moim 2250
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moim

Proof of Theorem moim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 imim1 70 . . . 4
21al2imi 1561 . . 3
32eximdv 1622 . 2
4 nfv 1619 . . 3  F/
54mo2 2233 . 2
6 nfv 1619 . . 3  F/
76mo2 2233 . 2
83, 5, 73imtr4g 261 1
Colors of variables: wff setvar class
Syntax hints:   wi 4  wal 1540  wex 1541   wceq 1642  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:  moimi  2251  euimmo  2253  moexex  2273  rmoim  3035  rmoimi2  3037  funmo  5125
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