Theorem simp3r2 1367

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

Assertion

Ref	Expression
simp3r2	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp3r2

Step	Hyp	Ref	Expression
1		simpr2 1236	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1130	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1072

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 197  df-an 385  df-3an 1074

This theorem is referenced by:  nllyrest  21489  cdlemblem  35580  cdleme21  36125  cdleme22b  36129  cdleme40m  36255  cdlemg34  36500  cdlemk5u  36649  cdlemk6u  36650  cdlemk21N  36661  cdlemk20  36662  cdlemk26b-3  36693  cdlemk26-3  36694  cdlemk28-3  36696  cdlemky  36714  cdlemk11t  36734  cdlemkyyN  36750  stoweidlem56  40774