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Theorem sbmo 2313
 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 2207 . . 3
2 nfv 1630 . . . . . 6
32sblim 2139 . . . . 5
43sbalv 2208 . . . 4
54exbii 1593 . . 3
61, 5bitri 242 . 2
7 nfv 1630 . . . 4
87mo2 2312 . . 3
98sbbii 1666 . 2
10 nfv 1630 . . 3
1110mo2 2312 . 2
126, 9, 113bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wex 1551  wsb 1659  wmo 2284 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288
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