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Theorem eubidv 1905
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 1418 . 2 xφ
2 eubidv.1 . 2 (φ → (ψχ))
31, 2eubid 1904 1 (φ → (∃!xψ∃!xχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  ∃!weu 1897
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
This theorem is referenced by:  eubii  1906  eueq2dc  2708  eueq3dc  2709  reuhypd  4169  feu  5015  funfveu  5131  dff4im  5256  acexmid  5454
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