Theorem exancom 1601

Description: Commutation of conjunction inside an existential quantifier. (Contributed by NM, 18-Aug-1993.)

Assertion

Ref	Expression
exancom	⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑))

Proof of Theorem exancom

Step	Hyp	Ref	Expression
1		ancom 264	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	exbii 1598	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑))

Syntax hints:   ∧ wa 103   ↔ wb 104  ∃wex 1485

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.29r  1614  19.42h  1680  19.42  1681  risset  2498  morex  2914  dfuni2  3798  eluni2  3800  unipr  3810  dfiun2g  3905  uniuni  4436  cnvco  4796  imadif  5278  funimaexglem  5281  pceu  12249  bdcuni  13911  bj-axun2  13950