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  14543  nllyrest  23680  bdayfinbndlem1  28697  cdlemblem  40608  cdleme21  41152  cdleme22b  41156  cdleme40m  41282  cdlemg34  41527  cdlemk5u  41676  cdlemk6u  41677  cdlemk21N  41688  cdlemk20  41689  cdlemk26b-3  41720  cdlemk26-3  41721  cdlemk28-3  41723  cdlemky  41741  cdlemk11t  41761  cdlemkyyN  41777  dihmeetlem20N  42141  stoweidlem56  46811