Theorem exancom 1608

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 266	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	exbii 1605	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∃wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.29r  1621  19.42h  1687  19.42  1688  risset  2505  morex  2923  dfuni2  3813  eluni2  3815  unipr  3825  dfiun2g  3920  uniuni  4453  cnvco  4814  imadif  5298  funimaexglem  5301  pceu  12297  bdcuni  14713  bj-axun2  14752