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Theorem mobidv 1933
 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 1418 . 2 xφ
2 mobidv.1 . 2 (φ → (ψχ))
31, 2mobid 1932 1 (φ → (∃*xψ∃*xχ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∃*wmo 1898 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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-eu 1900  df-mo 1901 This theorem is referenced by:  mobii  1934  mosubopt  4348  dffun6f  4858  funmo  4860  1stconst  5784  2ndconst  5785
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