Theorem simpr3l 1115

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpr3l	⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Proof of Theorem simpr3l

Step	Hyp	Ref	Expression
1		simp3l 1082	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	adantl 481	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by:  ax5seg  25618  axcont  25656  segconeq  31287  idinside  31361  btwnconn1lem10  31373  segletr  31391  cdlemc3  34498  cdlemc4  34499  cdleme1  34532  cdleme2  34533  cdleme3b  34534  cdleme3c  34535  cdleme3e  34537  cdleme27a  34673  stoweidlem56  38949