Theorem exancom 1570

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 1567	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑))

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