Theorem pm5.33 848

Description: Theorem *5.33 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.33	⊢ ((φ ∧ (ψ → χ)) ↔ (φ ∧ ((φ ∧ ψ) → χ)))

Proof of Theorem pm5.33

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 ⊢ (φ → (ψ ↔ (φ ∧ ψ)))
2	1	imbi1d 308	. 2 ⊢ (φ → ((ψ → χ) ↔ ((φ ∧ ψ) → χ)))
3	2	pm5.32i 618	1 ⊢ ((φ ∧ (ψ → χ)) ↔ (φ ∧ ((φ ∧ ψ) → χ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)