Theorem ancomd 263

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 262	. 2 ⊢ ((𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓))
3	1, 2	sylib 120	1 ⊢ (𝜑 → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  elres  4664  relbrcnvg  4724  fvelrnb  5242  relelec  6169  prcdnql  6674  1idpru  6781  gt0srpr  6925  dvdsdivcl  10250  nn0ehalf  10303  nn0oddm1d2  10309  nnoddm1d2  10310  coprmgcdb  10470  divgcdcoprm0  10483  divgcdcoprmex  10484  cncongr1  10485