Theorem simp3rr 1102

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3rr	⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Proof of Theorem simp3rr

Step	Hyp	Ref	Expression
1		simprr 537	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1051	1 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1009

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 1011

This theorem is referenced by:  prarloc  7864  tgqioo  15639  plyadd  15835  plymul  15836