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  8093  nosupbnd1lem5  27676  noinfbnd1lem5  27691  ax5seg  29007  axcont  29045  segconeq  36192  idinside  36266  btwnconn1lem10  36278  segletr  36296  cdlemc3  40639  cdlemc4  40640  cdleme1  40673  cdleme2  40674  cdleme3b  40675  cdleme3c  40676  cdleme3e  40678  cdleme27a  40813  stoweidlem56  46484  clnbgrgrimlem  48409