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Theorem exancom 1584
 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 264 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
21exbii 1581 1 (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ↔ wb 104  ∃wex 1469 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 1487  ax-ial 1511 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  19.29r  1597  19.42h  1663  19.42  1664  risset  2468  morex  2874  dfuni2  3748  eluni2  3750  unipr  3760  dfiun2g  3855  uniuni  4383  cnvco  4736  imadif  5215  funimaexglem  5218  bdcuni  13290  bj-axun2  13329
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