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  8095  nosupbnd1lem5  27692  noinfbnd1lem5  27707  ax5seg  29023  axcont  29061  segconeq  36223  idinside  36297  btwnconn1lem10  36309  segletr  36327  cdlemc3  40563  cdlemc4  40564  cdleme1  40597  cdleme2  40598  cdleme3b  40599  cdleme3c  40600  cdleme3e  40602  cdleme27a  40737  stoweidlem56  46408  clnbgrgrimlem  48287