Theorem simpl3 960

Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)

Assertion

Ref	Expression
simpl3	⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → χ)

Proof of Theorem simpl3

Step	Hyp	Ref	Expression
1		simp3 957	. 2 ⊢ ((φ ∧ ψ ∧ χ) → χ)
2	1	adantr 451	1 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → 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:  simpll3  996  simprl3  1002  simp1l3  1050  simp2l3  1056  simp3l3  1062  3anandirs  1284  tfinltfin  4501  enadj  6060  lemuc2  6254  lecadd2  6266