Theorem pm5.21im 338

Description: Two propositions are equivalent if they are both false. Closed form of 2false 339. Equivalent to a bi2 189-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 334	. 2 ⊢ (¬ φ → (¬ ψ ↔ (φ ↔ ψ)))
2	1	biimpd 198	1 ⊢ (¬ φ → (¬ ψ → (φ ↔ ψ)))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176

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

This theorem is referenced by:  pm5.21ndd  343  pm5.21  831