Theorem exancom 736

Description: Commutation of conjunction inside an existential quantifier.

Assertion

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

Proof of Theorem exancom

Step	Hyp	Ref	Expression
1		ancom 333	. 2 ⊢ ((φ ∧ ψ) ↔ (ψ ∧ φ))
2	1	biex 733	1 ⊢ (∃x(φ ∧ ψ) ↔ ∃x(ψ ∧ φ))

Syntax hints:   ↔ wb 127   ∧ wa 196  ∃wex 678

This theorem is referenced by:  19.29r 753  19.42 775  exan 784  risset 1235  pwpw0 1883  dfuni2 1921  eluni2 1923  unpr 1930  dfiun2 2014  imadif 2714  tz6.12-1 2842  chcmh 5148

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

metamath.org