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Theorem mobid 2238
 Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by NM, 8-Mar-1995.)
Hypotheses
Ref Expression
mobid.1 xφ
mobid.2 (φ → (ψχ))
Assertion
Ref Expression
mobid (φ → (∃*xψ∃*xχ))

Proof of Theorem mobid
StepHypRef Expression
1 mobid.1 . . . 4 xφ
2 mobid.2 . . . 4 (φ → (ψχ))
31, 2exbid 1773 . . 3 (φ → (xψxχ))
41, 2eubid 2211 . . 3 (φ → (∃!xψ∃!xχ))
53, 4imbi12d 311 . 2 (φ → ((xψ∃!xψ) ↔ (xχ∃!xχ)))
6 df-mo 2209 . 2 (∃*xψ ↔ (xψ∃!xψ))
7 df-mo 2209 . 2 (∃*xχ ↔ (xχ∃!xχ))
85, 6, 73bitr4g 279 1 (φ → (∃*xψ∃*xχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wex 1541  Ⅎwnf 1544  ∃!weu 2204  ∃*wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209 This theorem is referenced by:  mobidv  2239  euan  2261  rmobida  2798  rmoeq1f  2806
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