Theorem simpr3l 1235

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 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr3 1191	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

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:  poxp2  8142  nosupbnd1lem5  27676  noinfbnd1lem5  27691  ax5seg  28917  axcont  28955  segconeq  36028  idinside  36102  btwnconn1lem10  36114  segletr  36132  cdlemc3  40212  cdlemc4  40213  cdleme1  40246  cdleme2  40247  cdleme3b  40248  cdleme3c  40249  cdleme3e  40251  cdleme27a  40386  stoweidlem56  46085  clnbgrgrimlem  47946