Theorem simp23 1034

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

Assertion

Ref	Expression
simp23	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜃)

Proof of Theorem simp23

Step	Hyp	Ref	Expression
1		simp3 1001	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)
2	1	3ad2ant2 1021	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  simpl23  1079  simpr23  1088  simp123  1133  simp223  1142  simp323  1151  funtpg  5306