Theorem exancom 1499

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 253	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	exbii 1496	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑))

Syntax hints:   ∧ wa 97   ↔ wb 98  ∃wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  19.29r  1512  19.42h  1577  19.42  1578  risset  2352  morex  2725  dfuni2  3582  eluni2  3584  unipr  3594  dfiun2g  3689  uniuni  4183  cnvco  4520  imadif  4979  funimaexglem  4982  bdcuni  9996  bj-axun2  10035