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Theorem 2mos 2235
 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 2234 . 2
2 nfv 1609 . . . . . . 7
3 nfv 1609 . . . . . . . . . 10
43sbrim 2020 . . . . . . . . 9
5 nfv 1609 . . . . . . . . . 10
6 2mos.1 . . . . . . . . . . . 12
76expcom 424 . . . . . . . . . . 11
87pm5.74d 238 . . . . . . . . . 10
95, 8sbie 1991 . . . . . . . . 9
104, 9bitr3i 242 . . . . . . . 8
1110pm5.74ri 237 . . . . . . 7
122, 11sbie 1991 . . . . . 6
1312anbi2i 675 . . . . 5
1413imbi1i 315 . . . 4
15142albii 1557 . . 3
16152albii 1557 . 2
171, 16bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wex 1531   wceq 1632  wsb 1638 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-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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