Theorem pm5.21im 378

Description: Two propositions are equivalent if they are both false. Closed form of 2false 379. Equivalent to a biimpr 223-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.)

Assertion

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

Proof of Theorem pm5.21im

Step	Hyp	Ref	Expression
1		nbn2 374	. 2 ⊢ (¬ 𝜑 → (¬ 𝜓 ↔ (𝜑 ↔ 𝜓)))
2	1	biimpd 232	1 ⊢ (¬ 𝜑 → (¬ 𝜓 → (𝜑 ↔ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 209

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 210

This theorem is referenced by:  pm5.21ndd  384  pm5.21  825