Theorem bnj258 33548

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj258	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒))

Proof of Theorem bnj258

Step	Hyp	Ref	Expression
1		bnj257 33547	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒))
2		df-bnj17 33527	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒))
3	1, 2	bitri 274	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒))

Syntax hints:   ↔ wb 205   ∧ wa 396   ∧ w3a 1087   ∧ w-bnj17 33526

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 397  df-3an 1089  df-bnj17 33527

This theorem is referenced by:  bnj707  33595  bnj1019  33619  bnj556  33740  bnj594  33752  bnj1018g  33803  bnj1018  33804  bnj1110  33822