Theorem 3simpa 952

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

Assertion

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

Proof of Theorem 3simpa

Step	Hyp	Ref	Expression
1		df-3an 936	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ))
2	1	simplbi 446	1 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ ψ))

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:  3simpb  953  3simpc  954  simp1  955  simp2  956  3adant3  975  3adantl3  1113  3adantr3  1116  sfintfin  4533  peano4  4558  ovig  5598  ovmpt2x  5713  ce0nnulb  6183  fce  6189