Theorem ferison 2315

Description: "Ferison", one of the syllogisms of Aristotelian logic. No φ is ψ, and some φ is χ, therefore some χ is not ψ. (In Aristotelian notation, EIO-3: MeP and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)

Hypotheses

Ref	Expression
ferison.maj	⊢ ∀x(φ → ¬ ψ)
ferison.min	⊢ ∃x(φ ∧ χ)

Assertion

Ref	Expression
ferison	⊢ ∃x(χ ∧ ¬ ψ)

Proof of Theorem ferison

Step	Hyp	Ref	Expression
1		ferison.maj	. 2 ⊢ ∀x(φ → ¬ ψ)
2		ferison.min	. 2 ⊢ ∃x(φ ∧ χ)
3	1, 2	datisi 2313	1 ⊢ ∃x(χ ∧ ¬ ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by: (None)