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Theorem exancom 1515
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 257 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
21exbii 1512 1 (∃𝑥(𝜑𝜓) ↔ ∃𝑥(𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  19.29r  1528  19.42h  1593  19.42  1594  risset  2369  morex  2747  dfuni2  3609  eluni2  3611  unipr  3621  dfiun2g  3716  uniuni  4210  cnvco  4547  imadif  5006  funimaexglem  5009  bdcuni  10362  bj-axun2  10401
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