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Theorem euanv 1954
 Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euanv (∃!x(φ ψ) ↔ (φ ∃!xψ))
Distinct variable group:   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem euanv
StepHypRef Expression
1 ax-17 1416 . 2 (φxφ)
21euan 1953 1 (∃!x(φ ψ) ↔ (φ ∃!xψ))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901 This theorem is referenced by:  eueq2dc  2708  fsn  5278
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