Theorem pm5.21 837

Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.)

Assertion

Ref	Expression
pm5.21	⊢ ((¬ 𝜑 ∧ ¬ 𝜓) → (𝜑 ↔ 𝜓))

Proof of Theorem pm5.21

Step	Hyp	Ref	Expression
1		pm5.21im 377	. 2 ⊢ (¬ 𝜑 → (¬ 𝜓 → (𝜑 ↔ 𝜓)))
2	1	imp 412	1 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) → (𝜑 ↔ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∧ wa 401

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

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  onsuct0  37229  bj-axseprep  37990  wl-nfeqfb  38469  tsbi2  39067