Theorem simp3r1 1282

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

Assertion

Ref	Expression
simp3r1	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simp3r1

Step	Hyp	Ref	Expression
1		simpr1 1195	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  nllyrest  23373  segletr  36102  cdlemblem  39787  cdleme21  40331  cdleme22b  40335  cdleme40m  40461  cdlemg34  40706  cdlemk5u  40855  cdlemk6u  40856  cdlemk21N  40867  cdlemk20  40868  cdlemk26b-3  40899  cdlemk26-3  40900  cdlemk28-3  40902  cdlemk37  40908  cdlemky  40920  cdlemk11t  40940  cdlemkyyN  40956  dihmeetlem20N  41320  stoweidlem56  46054