Theorem ancomd 267

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 266	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓))
3	1, 2	sylib 122	1 ⊢ (𝜑 → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  elres  4983  relbrcnvg  5049  fvelrnb  5611  relelec  6643  prcdnql  7568  1idpru  7675  gt0srpr  7832  fihashf1rn  10897  prodmodclem3  11757  sinbnd  11934  cosbnd  11935  dvdsdivcl  12032  nn0ehalf  12085  nn0oddm1d2  12091  nnoddm1d2  12092  coprmgcdb  12281  divgcdcoprm0  12294  divgcdcoprmex  12295  cncongr1  12296  quscrng  14165  sincosq2sgn  15147  sincosq4sgn  15149