Theorem simpr3l 1247

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr3l	⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Proof of Theorem simpr3l

Step	Hyp	Ref	Expression
1		simprl 780	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr3 1203	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  poxp2  8118  nosupbnd1lem5  27753  noinfbnd1lem5  27768  ax5seg  29085  axcont  29123  segconeq  36324  idinside  36398  btwnconn1lem10  36410  segletr  36428  cdlemc3  40781  cdlemc4  40782  cdleme1  40815  cdleme2  40816  cdleme3b  40817  cdleme3c  40818  cdleme3e  40820  cdleme27a  40955  stoweidlem56  46594  clnbgrgrimlem  48519