Theorem simp3r 984

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp3r	⊢ ((φ ∧ ψ ∧ (χ ∧ θ)) → θ)

Proof of Theorem simp3r

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((χ ∧ θ) → θ)
2	1	3ad2ant3 978	1 ⊢ ((φ ∧ ψ ∧ (χ ∧ θ)) → θ)

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:  simpl3r  1011  simpr3r  1017  simp13r  1071  simp23r  1077  simp33r  1083  ssfin  4471  tfinltfinlem1  4501  nnpweq  4524  sfinltfin  4536  funprgOLD  5151  f1oiso2  5501