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Theorem eubidv 1886
Description: Formula-building rule for uniqueness quantifier (deduction rule). (Contributed by NM, 9-Jul-1994.)
Hypothesis
Ref Expression
eubidv.1 (φ → (ψχ))
Assertion
Ref Expression
eubidv (φ → (∃!xψ∃!xχ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)

Proof of Theorem eubidv
StepHypRef Expression
1 nfv 1398 . 2 xφ
2 eubidv.1 . 2 (φ → (ψχ))
31, 2eubid 1885 1 (φ → (∃!xψ∃!xχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  ∃!weu 1878
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-17 1396  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-eu 1881
This theorem is referenced by:  eubii  1887  eueq2dc  2687  eueq3dc  2688  reuhypd  4149  feu  4993  funfveu  5109  dff4im  5234  acexmid  5431
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