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Theorem mobidv 2239
 Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
mobidv.1 (φ → (ψχ))
Assertion
Ref Expression
mobidv (φ → (∃*xψ∃*xχ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)

Proof of Theorem mobidv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 mobidv.1 . 2 (φ → (ψχ))
31, 2mobid 2238 1 (φ → (∃*xψ∃*xχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃*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:  mobii  2240  mosubopt  4612  dffun6f  5123  funmo  5125
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