Theorem simp3r2 1301

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

Assertion

Ref	Expression
simp3r2	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp3r2

Step	Hyp	Ref	Expression
1		simpr2 1214	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

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:  nllyrest  23624  bdayfinbndlem1  28641  cdlemblem  40548  cdleme21  41092  cdleme22b  41096  cdleme40m  41222  cdlemg34  41467  cdlemk5u  41616  cdlemk6u  41617  cdlemk21N  41628  cdlemk20  41629  cdlemk26b-3  41660  cdlemk26-3  41661  cdlemk28-3  41663  cdlemky  41681  cdlemk11t  41701  cdlemkyyN  41717  stoweidlem56  46753