Theorem an12s 499

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 495 is combined with syl 14 (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 495	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		an12s.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylbi 114	1 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  anabsan2  518  1stconst  5842  2ndconst  5843  iccshftr  8862  iccshftl  8864  iccdil  8866  icccntr  8868