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Theorem 2mos 2283
 Description: Double "exists at most one", using implicit substitution. (Contributed by NM, 10-Feb-2005.)
Hypothesis
Ref Expression
2mos.1
Assertion
Ref Expression
2mos
Distinct variable groups:   ,,   ,,   ,,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem 2mos
StepHypRef Expression
1 2mo 2282 . 2
2 nfv 1619 . . . . . . 7
3 nfv 1619 . . . . . . . . . 10
43sbrim 2067 . . . . . . . . 9
5 nfv 1619 . . . . . . . . . 10
6 2mos.1 . . . . . . . . . . . 12
76expcom 424 . . . . . . . . . . 11
87pm5.74d 238 . . . . . . . . . 10
95, 8sbie 2038 . . . . . . . . 9
104, 9bitr3i 242 . . . . . . . 8
1110pm5.74ri 237 . . . . . . 7
122, 11sbie 2038 . . . . . 6
1312anbi2i 675 . . . . 5
1413imbi1i 315 . . . 4
15142albii 1567 . . 3
16152albii 1567 . 2
171, 16bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541   wceq 1642  wsb 1648 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by: (None)
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