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Theorem mo2 2293
Description: Alternate definition of "at most one." (Contributed by NM, 8-Mar-1995.) Restrict dummy variable z. (Revised by Wolf Lammen, 28-May-2019.)
Hypothesis
Ref Expression
mo2.1
Assertion
Ref Expression
mo2
Distinct variable group:   ,

Proof of Theorem mo2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mo2v 2289 . 2
2 mo2.1 . . . . 5
3 nfv 1707 . . . . 5
42, 3nfim 1920 . . . 4
54nfal 1947 . . 3
6 nfv 1707 . . 3
7 equequ2 1799 . . . . 5
87imbi2d 316 . . . 4
98albidv 1713 . . 3
105, 6, 9cbvex 2022 . 2
111, 10bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616  E*wmo 2283
This theorem is referenced by:  mo3  2323  mo3OLD  2324  mo  2325  eu5OLD  2330  morimvOLD  2342  rmo2  3427  nmo  27384  bj-eu3f  34413
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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