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Theorem sbmo 2186
 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 2080 . . 3
2 nfv 1609 . . . . . 6
32sblim 2021 . . . . 5
43sbalv 2081 . . . 4
54exbii 1572 . . 3
61, 5bitri 240 . 2
7 nfv 1609 . . . 4
87mo2 2185 . . 3
98sbbii 1643 . 2
10 nfv 1609 . . 3
1110mo2 2185 . 2
126, 9, 113bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530  wex 1531   wceq 1632  wsb 1638  wmo 2157 This theorem is referenced by:  sbmoOLD  26442 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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