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Theorem exancom 1608
Description: Commutation of conjunction inside an existential quantifier. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
exancom (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))

Proof of Theorem exancom
StepHypRef Expression
1 ancom 266 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
21exbii 1605 1 (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wa 104  wb 105  wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  19.29r  1621  19.42h  1687  19.42  1688  risset  2505  morex  2923  dfuni2  3813  eluni2  3815  unipr  3825  dfiun2g  3920  uniuni  4453  cnvco  4814  imadif  5298  funimaexglem  5301  pceu  12297  bdcuni  14667  bj-axun2  14706
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