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Theorem eubidv 1985
Description: Formula-building rule for unique existential quantifier (deduction form). (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 1493 . 2 𝑥𝜑
2 eubidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2eubid 1984 1 (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  ∃!weu 1977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-eu 1980
This theorem is referenced by:  eubii  1986  eueq2dc  2830  eueq3dc  2831  reuhypd  4362  feu  5275  funfveu  5402  dff4im  5534  acexmid  5741  upxp  12368  dedekindicc  12707
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