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Theorem mo2 2233
 Description: Alternate definition of "at most one." (Contributed by NM, 8-Mar-1995.)
Hypothesis
Ref Expression
mo2.1
Assertion
Ref Expression
mo2
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem mo2
StepHypRef Expression
1 df-mo 2209 . 2
2 alnex 1543 . . . . 5
3 pm2.21 100 . . . . . . 7
43alimi 1559 . . . . . 6
5 19.8a 1756 . . . . . 6
64, 5syl 15 . . . . 5
72, 6sylbir 204 . . . 4
8 mo2.1 . . . . 5
98eumo0 2228 . . . 4
107, 9ja 153 . . 3
118eu3 2230 . . . 4
1211simplbi2com 1374 . . 3
1310, 12impbii 180 . 2
141, 13bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wex 1541  wnf 1544  weu 2204  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:  sbmo  2234  mo3  2235  eu5  2242  moim  2250  morimv  2252  moanim  2260  mo2icl  3015  rmo2  3131  dffun3  5120  dffun6f  5123
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