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  8086  nosupbnd1lem5  27690  noinfbnd1lem5  27705  ax5seg  29021  axcont  29059  segconeq  36208  idinside  36282  btwnconn1lem10  36294  segletr  36312  cdlemc3  40653  cdlemc4  40654  cdleme1  40687  cdleme2  40688  cdleme3b  40689  cdleme3c  40690  cdleme3e  40692  cdleme27a  40827  stoweidlem56  46502  clnbgrgrimlem  48421