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))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  elres  5099  relbrcnvg  5166  fvelrnb  5750  relelec  6849  prcdnql  7852  1idpru  7959  gt0srpr  8116  fihashf1rn  11242  pfxccatin12  11520  prodmodclem3  12360  sinbnd  12537  cosbnd  12538  dvdsdivcl  12635  nn0ehalf  12688  nn0oddm1d2  12694  nnoddm1d2  12695  coprmgcdb  12884  divgcdcoprm0  12897  divgcdcoprmex  12898  cncongr1  12899  quscrng  14921  sincosq2sgn  15981  sincosq4sgn  15983  subupgr  16636