Theorem simpr3l 1236

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 771	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr3 1192	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

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:  poxp2  8097  nosupbnd1lem5  27697  noinfbnd1lem5  27712  ax5seg  29029  axcont  29067  segconeq  36232  idinside  36306  btwnconn1lem10  36318  segletr  36336  cdlemc3  40598  cdlemc4  40599  cdleme1  40632  cdleme2  40633  cdleme3b  40634  cdleme3c  40635  cdleme3e  40637  cdleme27a  40772  stoweidlem56  46443  clnbgrgrimlem  48322