Theorem simp3r3 1302

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 1215	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  hash7g  14634  nllyrest  23810  bdayfinbndlem1  28858  cdlemblem  40943  cdleme21  41487  cdleme22b  41491  cdleme40m  41617  cdlemg34  41862  cdlemk5u  42011  cdlemk6u  42012  cdlemk21N  42023  cdlemk20  42024  cdlemk26b-3  42055  cdlemk26-3  42056  cdlemk28-3  42058  cdlemky  42076  cdlemk11t  42096  cdlemkyyN  42112  dihmeetlem20N  42476  stoweidlem56  47159