Theorem pm5.42 531

Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.42	⊢ ((φ → (ψ → χ)) ↔ (φ → (ψ → (φ ∧ χ))))

Proof of Theorem pm5.42

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 ⊢ (φ → (χ ↔ (φ ∧ χ)))
2	1	imbi2d 307	. 2 ⊢ (φ → ((ψ → χ) ↔ (ψ → (φ ∧ χ))))
3	2	pm5.74i 236	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:  anc2l  538  imdistan  670