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Theorem sbmo 2234
 Description: Substitution into "at most one". (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
sbmo
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbmo
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbex 2128 . . 3
2 nfv 1619 . . . . . 6
32sblim 2068 . . . . 5
43sbalv 2129 . . . 4
54exbii 1582 . . 3
61, 5bitri 240 . 2
7 nfv 1619 . . . 4
87mo2 2233 . . 3
98sbbii 1653 . 2
10 nfv 1619 . . 3
1110mo2 2233 . 2
126, 9, 113bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540  wex 1541   wceq 1642  wsb 1648  wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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: (None)
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