Theorem 3simpb 953

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

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

Proof of Theorem 3simpb

Step	Hyp	Ref	Expression
1		3ancomb 943	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ χ ∧ ψ))
2		3simpa 952	. 2 ⊢ ((φ ∧ χ ∧ ψ) → (φ ∧ χ))
3	1, 2	sylbi 187	1 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ χ))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by:  3adant2  974  3adantl2  1112  3adantr2  1115