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 771	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr3 1191	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  8168  nosupbnd1lem5  27757  noinfbnd1lem5  27772  ax5seg  28953  axcont  28991  segconeq  36011  idinside  36085  btwnconn1lem10  36097  segletr  36115  cdlemc3  40195  cdlemc4  40196  cdleme1  40229  cdleme2  40230  cdleme3b  40231  cdleme3c  40232  cdleme3e  40234  cdleme27a  40369  stoweidlem56  46071  clnbgrgrimlem  47901