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Theorem mobidv 1918
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 1402 . 2 xφ
2 mobidv.1 . 2 (φ → (ψχ))
31, 2mobid 1917 1 (φ → (∃*xψ∃*xχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  ∃*wmo 1883
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-eu 1885  df-mo 1886
This theorem is referenced by:  mobii  1919  mosubopt  4332  dffun6f  4841  funmo  4843  1stconst  5765  2ndconst  5766
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