Theorem simp3r3 1296

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 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1147	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  hash7g  14496  nllyrest  23526  bdayfinbndlem1  28537  cdlemblem  40381  cdleme21  40925  cdleme22b  40929  cdleme40m  41055  cdlemg34  41300  cdlemk5u  41449  cdlemk6u  41450  cdlemk21N  41461  cdlemk20  41462  cdlemk26b-3  41493  cdlemk26-3  41494  cdlemk28-3  41496  cdlemky  41514  cdlemk11t  41534  cdlemkyyN  41550  dihmeetlem20N  41914  stoweidlem56  46594