Theorem simp3r3 1164

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 1062	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1077	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by:  nllyrest  21099  cdlemblem  34097  cdleme21  34643  cdleme22b  34647  cdleme40m  34773  cdlemg34  35018  cdlemk5u  35167  cdlemk6u  35168  cdlemk21N  35179  cdlemk20  35180  cdlemk26b-3  35211  cdlemk26-3  35212  cdlemk28-3  35214  cdlemky  35232  cdlemk11t  35252  cdlemkyyN  35268  dihmeetlem20N  35633  stoweidlem56  38949