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)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1105

This theorem is referenced by:  hash7g  14525  nllyrest  23624  bdayfinbndlem1  28638  cdlemblem  40545  cdleme21  41089  cdleme22b  41093  cdleme40m  41219  cdlemg34  41464  cdlemk5u  41613  cdlemk6u  41614  cdlemk21N  41625  cdlemk20  41626  cdlemk26b-3  41657  cdlemk26-3  41658  cdlemk28-3  41660  cdlemky  41678  cdlemk11t  41698  cdlemkyyN  41714  dihmeetlem20N  42078  stoweidlem56  46750