Theorem pm5.3 692

Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm5.3	⊢ (((φ ∧ ψ) → χ) ↔ ((φ ∧ ψ) → (φ ∧ χ)))

Proof of Theorem pm5.3

Step	Hyp	Ref	Expression
1		impexp 433	. 2 ⊢ (((φ ∧ ψ) → χ) ↔ (φ → (ψ → χ)))
2		imdistan 670	. 2 ⊢ ((φ → (ψ → χ)) ↔ ((φ ∧ ψ) → (φ ∧ χ)))
3	1, 2	bitri 240	1 ⊢ (((φ ∧ ψ) → χ) ↔ ((φ ∧ ψ) → (φ ∧ χ)))

Syntax hints:   → wi 4   ↔ wb 176   ∧ 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)