Theorem an12s 649

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 645 is combined with syl 17 (or a variant). (Contributed by NM, 13-Mar-1996.)

Hypothesis

Ref	Expression
an12s.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Assertion

Ref	Expression
an12s	⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) → 𝜃)

Proof of Theorem an12s

Step	Hyp	Ref	Expression
1		an12 645	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		an12s.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylbi 217	1 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  anabsan2  674  oecl  8575  oaass  8599  odi  8617  oen0  8624  oeworde  8631  ltexprlem4  11079  iccshftr  13526  iccshftl  13528  iccdil  13530  icccntr  13532  ndvdsadd  16447  eulerthlem2  16819  neips  23121  tx1stc  23658  filuni  23893  ufldom  23970  isch3  31260  unoplin  31939  hmoplin  31961  adjlnop  32105  chirredlem2  32410  btwnconn1lem12  36099  btwnconn1  36102  finxpreclem2  37391  poimirlem25  37652  mblfinlem4  37667  iscringd  38005  unichnidl  38038