Theorem ancomd 258

Description: Commutation of conjuncts in consequent. (Contributed by Jeff Hankins, 14-Aug-2009.)

Hypothesis

Ref	Expression
ancomd.1	⊢ (𝜑 → (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
ancomd	⊢ (𝜑 → (𝜒 ∧ 𝜓))

Proof of Theorem ancomd

Step	Hyp	Ref	Expression
1		ancomd.1	. 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒))
2		ancom 257	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓))
3	1, 2	sylib 131	1 ⊢ (𝜑 → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 101

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105

This theorem depends on definitions:  df-bi 114

This theorem is referenced by:  elres  4671  relbrcnvg  4729  fvelrnb  5246  relelec  6174  prcdnql  6610  1idpru  6717  gt0srpr  6861  dvdsdivcl  10125  nn0ehalf  10178  nn0oddm1d2  10184  nnoddm1d2  10185