Theorem simp32 975

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

Assertion

Ref	Expression
simp32	⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃)

Proof of Theorem simp32

Step	Hyp	Ref	Expression
1		simp2 939	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜃)
2	1	3ad2ant3 961	1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  simpl32  1020  simpr32  1029  simp132  1074  simp232  1083  simp332  1092