Theorem simp2r3 1296

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

Assertion

Ref	Expression
simp2r3	⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒)

Proof of Theorem simp2r3

Step	Hyp	Ref	Expression
1		simpr3 1215	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant2 1152	1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  poxp3  8147  hash7g  14525  btwnconn1lem8  36567  btwnconn1lem9  36568  btwnconn1lem10  36569  btwnconn1lem11  36570  btwnconn1lem12  36571  cdlemj3  41578  jm2.27  43718  iunrelexpmin2  44421