Theorem simp2lr 1248

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 774	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1140	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  fpr3g  8232  tfrlem5  8316  omeu  8517  expmordi  14127  4sqlem18  16931  vdwlem10  16959  mvrf1  21967  mdetuni0  22611  mdetmul  22613  tsmsxp  24145  ax5seglem3  29025  btwnconn1lem1  36322  btwnconn1lem3  36324  btwnconn1lem4  36325  btwnconn1lem5  36326  btwnconn1lem6  36327  btwnconn1lem7  36328  linethru  36388  lshpkrlem6  39614  athgt  39955  2llnjN  40066  dalaw  40385  cdlemb2  40540  4atexlemex6  40573  cdleme01N  40720  cdleme0ex2N  40723  cdleme7aa  40741  cdleme7e  40746  cdlemg33c0  41201  dihmeetlem3N  41804  pellex  43287