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  14658  nllyrest  23835  bdayfinbndlem1  28883  cdlemblem  41042  cdleme21  41586  cdleme22b  41590  cdleme40m  41716  cdlemg34  41961  cdlemk5u  42110  cdlemk6u  42111  cdlemk21N  42122  cdlemk20  42123  cdlemk26b-3  42154  cdlemk26-3  42155  cdlemk28-3  42157  cdlemky  42175  cdlemk11t  42195  cdlemkyyN  42211  dihmeetlem20N  42575  stoweidlem56  47271