Theorem simp3r3 1302

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

Assertion

Ref	Expression
simp3r3	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp3r3

Step	Hyp	Ref	Expression
1		simpr3 1215	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  hash7g  14555  nllyrest  23718  bdayfinbndlem1  28740  cdlemblem  40674  cdleme21  41218  cdleme22b  41222  cdleme40m  41348  cdlemg34  41593  cdlemk5u  41742  cdlemk6u  41743  cdlemk21N  41754  cdlemk20  41755  cdlemk26b-3  41786  cdlemk26-3  41787  cdlemk28-3  41789  cdlemky  41807  cdlemk11t  41827  cdlemkyyN  41843  dihmeetlem20N  42207  stoweidlem56  46892