Theorem bnj1224 32073

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj1224.1	⊢ ¬ (𝜃 ∧ 𝜏 ∧ 𝜂)

Assertion

Ref	Expression
bnj1224	⊢ ((𝜃 ∧ 𝜏) → ¬ 𝜂)

Proof of Theorem bnj1224

Step	Hyp	Ref	Expression
1		bnj1224.1	. . 3 ⊢ ¬ (𝜃 ∧ 𝜏 ∧ 𝜂)
2		df-3an 1085	. . 3 ⊢ ((𝜃 ∧ 𝜏 ∧ 𝜂) ↔ ((𝜃 ∧ 𝜏) ∧ 𝜂))
3	1, 2	mtbi 324	. 2 ⊢ ¬ ((𝜃 ∧ 𝜏) ∧ 𝜂)
4	3	imnani 403	1 ⊢ ((𝜃 ∧ 𝜏) → ¬ 𝜂)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  bnj1204  32284  bnj1279  32290