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Theorem eubidv 2008
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 1509 . 2 𝑥𝜑
2 eubidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2eubid 2007 1 (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  ∃!weu 2000
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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-eu 2003
This theorem is referenced by:  eubii  2009  eueq2dc  2860  eueq3dc  2861  reuhypd  4398  feu  5311  funfveu  5440  dff4im  5572  acexmid  5779  upxp  12473  dedekindicc  12812
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