Theorem simp1r 980

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

Assertion

Ref	Expression
simp1r	⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → ψ)

Proof of Theorem simp1r

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((φ ∧ ψ) → ψ)
2	1	3ad2ant1 976	1 ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → 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:  simpl1r  1007  simpr1r  1013  simp11r  1067  simp21r  1073  simp31r  1079  vtoclgft  2906  nndisjeq  4430  ncfindi  4476  nnadjoinpw  4522  nnpweq  4524  sfinltfin  4536