Theorem simp2r3 1294

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 1213	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant2 1150	1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 1103

This theorem is referenced by:  poxp3  8134  hash7g  14513  btwnconn1lem8  36457  btwnconn1lem9  36458  btwnconn1lem10  36459  btwnconn1lem11  36460  btwnconn1lem12  36461  cdlemj3  41459  jm2.27  43597  iunrelexpmin2  44300