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Theorem eubidv 2212
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 1619 . 2 xφ
2 eubidv.1 . 2 (φ → (ψχ))
31, 2eubid 2211 1 (φ → (∃!xψ∃!xχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  ∃!weu 2204
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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
This theorem is referenced by:  eubii  2213  eueq2  3010  eueq3  3011  moeq3  3013  fneu  5187  feu  5242  dff4  5421  scancan  6331
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