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Theorem exancom 1570
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 1567 1 (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  wex 1451
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.29r  1583  19.42h  1648  19.42  1649  risset  2437  morex  2837  dfuni2  3704  eluni2  3706  unipr  3716  dfiun2g  3811  uniuni  4332  cnvco  4684  imadif  5161  funimaexglem  5164  bdcuni  12766  bj-axun2  12805
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