Theorem simp3r1 1261

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 1174	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1115	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 387   ∧ w3a 1068

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 199  df-an 388  df-3an 1070

This theorem is referenced by:  nllyrest  21788  segletr  33036  cdlemblem  36322  cdleme21  36866  cdleme22b  36870  cdleme40m  36996  cdlemg34  37241  cdlemk5u  37390  cdlemk6u  37391  cdlemk21N  37402  cdlemk20  37403  cdlemk26b-3  37434  cdlemk26-3  37435  cdlemk28-3  37437  cdlemk37  37443  cdlemky  37455  cdlemk11t  37475  cdlemkyyN  37491  dihmeetlem20N  37855  stoweidlem56  41718