Theorem simpr3l 1233

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 1189	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  8167  nosupbnd1lem5  27772  noinfbnd1lem5  27787  ax5seg  28968  axcont  29006  segconeq  35992  idinside  36066  btwnconn1lem10  36078  segletr  36096  cdlemc3  40176  cdlemc4  40177  cdleme1  40210  cdleme2  40211  cdleme3b  40212  cdleme3c  40213  cdleme3e  40215  cdleme27a  40350  stoweidlem56  46012  clnbgrgrimlem  47839