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  8079  nosupbnd1lem5  27652  noinfbnd1lem5  27667  ax5seg  28918  axcont  28956  segconeq  36075  idinside  36149  btwnconn1lem10  36161  segletr  36179  cdlemc3  40312  cdlemc4  40313  cdleme1  40346  cdleme2  40347  cdleme3b  40348  cdleme3c  40349  cdleme3e  40351  cdleme27a  40486  stoweidlem56  46178  clnbgrgrimlem  48057