Theorem pm3.37 562

Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)

Assertion

Ref	Expression
pm3.37	⊢ (((φ ∧ ψ) → χ) → ((φ ∧ ¬ χ) → ¬ ψ))

Proof of Theorem pm3.37

Step	Hyp	Ref	Expression
1		pm4.14 561	. 2 ⊢ (((φ ∧ ψ) → χ) ↔ ((φ ∧ ¬ χ) → ¬ ψ))
2	1	biimpi 186	1 ⊢ (((φ ∧ ψ) → χ) → ((φ ∧ ¬ χ) → ¬ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by: (None)