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  8122  nosupbnd1lem5  27624  noinfbnd1lem5  27639  ax5seg  28865  axcont  28903  segconeq  35998  idinside  36072  btwnconn1lem10  36084  segletr  36102  cdlemc3  40187  cdlemc4  40188  cdleme1  40221  cdleme2  40222  cdleme3b  40223  cdleme3c  40224  cdleme3e  40226  cdleme27a  40361  stoweidlem56  46054  clnbgrgrimlem  47933