Theorem exancom 1586

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 437	. 2 ⊢ ((φ ∧ ψ) ↔ (ψ ∧ φ))
2	1	exbii 1582	1 ⊢ (∃x(φ ∧ ψ) ↔ ∃x(ψ ∧ φ))

Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  19.29r  1597  19.42  1880  risset  2662  morex  3021  pwpw0  3856  pwsnALT  3883  dfuni2  3894  eluni2  3896  unipr  3906  dfiun2g  4000  dfimak2  4299  insklem  4305  el1st  4730  setconslem6  4737  dfcnv2  5101  imadif  5172  addcfnex  5825  addccan2nclem1  6264