Theorem simp2lr 1242

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

Assertion

Ref	Expression
simp2lr	⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Proof of Theorem simp2lr

Step	Hyp	Ref	Expression
1		simplr 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1134	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  fpr3g  8284  tfrlem5  8394  omeu  8597  expmordi  14185  4sqlem18  16982  vdwlem10  17010  mvrf1  21946  mdetuni0  22559  mdetmul  22561  tsmsxp  24093  ax5seglem3  28910  btwnconn1lem1  36105  btwnconn1lem3  36107  btwnconn1lem4  36108  btwnconn1lem5  36109  btwnconn1lem6  36110  btwnconn1lem7  36111  linethru  36171  lshpkrlem6  39133  athgt  39475  2llnjN  39586  dalaw  39905  cdlemb2  40060  4atexlemex6  40093  cdleme01N  40240  cdleme0ex2N  40243  cdleme7aa  40261  cdleme7e  40266  cdlemg33c0  40721  dihmeetlem3N  41324  pellex  42858