Theorem simp3r3 1285

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 1198	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  hash7g  14421  nllyrest  23442  bdayfinbndlem1  28475  cdlemblem  40163  cdleme21  40707  cdleme22b  40711  cdleme40m  40837  cdlemg34  41082  cdlemk5u  41231  cdlemk6u  41232  cdlemk21N  41243  cdlemk20  41244  cdlemk26b-3  41275  cdlemk26-3  41276  cdlemk28-3  41278  cdlemky  41296  cdlemk11t  41316  cdlemkyyN  41332  dihmeetlem20N  41696  stoweidlem56  46408