Theorem simp32 1065

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 1029	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜃)
2	1	3ad2ant3 1051	1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  simpl32  1110  simpr32  1119  simp132  1164  simp232  1173  simp332  1182  bitsfzo  12722