Theorem simp3r2 1299

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 1212	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1151	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 1103

This theorem is referenced by:  nllyrest  23608  bdayfinbndlem1  28622  cdlemblem  40452  cdleme21  40996  cdleme22b  41000  cdleme40m  41126  cdlemg34  41371  cdlemk5u  41520  cdlemk6u  41521  cdlemk21N  41532  cdlemk20  41533  cdlemk26b-3  41564  cdlemk26-3  41565  cdlemk28-3  41567  cdlemky  41585  cdlemk11t  41605  cdlemkyyN  41621  stoweidlem56  46655