Theorem simp21 988

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)

Assertion

Ref	Expression
simp21	⊢ ((φ ∧ (ψ ∧ χ ∧ θ) ∧ τ) → ψ)

Proof of Theorem simp21

Step	Hyp	Ref	Expression
1		simp1 955	. 2 ⊢ ((ψ ∧ χ ∧ θ) → ψ)
2	1	3ad2ant2 977	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ) ∧ τ) → ψ)

Syntax hints:   → wi 4   ∧ 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:  simpl21  1033  simpr21  1042  simp121  1087  simp221  1096  simp321  1105  sfinltfin  4535