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)

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:  nllyrest  23798  bdayfinbndlem1  28846  cdlemblem  40830  cdleme21  41374  cdleme22b  41378  cdleme40m  41504  cdlemg34  41749  cdlemk5u  41898  cdlemk6u  41899  cdlemk21N  41910  cdlemk20  41911  cdlemk26b-3  41942  cdlemk26-3  41943  cdlemk28-3  41945  cdlemky  41963  cdlemk11t  41983  cdlemkyyN  41999  stoweidlem56  47035