Theorem 3simpc 954

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
3simpc	⊢ ((φ ∧ ψ ∧ χ) → (ψ ∧ χ))

Proof of Theorem 3simpc

Step	Hyp	Ref	Expression
1		3anrot 939	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ χ ∧ φ))
2		3simpa 952	. 2 ⊢ ((ψ ∧ χ ∧ φ) → (ψ ∧ χ))
3	1, 2	sylbi 187	1 ⊢ ((φ ∧ ψ ∧ χ) → (ψ ∧ χ))

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  simp3  957  3adant1  973  3adantl1  1111  3adantr1  1114  eupickb  2269