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 397   ∧ w3a 1088

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 206  df-an 398  df-3an 1090

This theorem is referenced by:  poxp2  8129  nosupbnd1lem5  27215  noinfbnd1lem5  27230  ax5seg  28196  axcont  28234  segconeq  34982  idinside  35056  btwnconn1lem10  35068  segletr  35086  cdlemc3  39064  cdlemc4  39065  cdleme1  39098  cdleme2  39099  cdleme3b  39100  cdleme3c  39101  cdleme3e  39103  cdleme27a  39238  stoweidlem56  44772