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Theorem exancom 1540
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 262 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
21exbii 1537 1 (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wa 102  wb 103  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.29r  1553  19.42h  1618  19.42  1619  risset  2400  morex  2787  dfuni2  3629  eluni2  3631  unipr  3641  dfiun2g  3736  uniuni  4237  cnvco  4579  imadif  5047  funimaexglem  5050  bdcuni  11110  bj-axun2  11149
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