Theorem nanan 1289

Description: Write 'and' in terms of 'nand'. (Contributed by Mario Carneiro, 9-May-2015.)

Assertion

Ref	Expression
nanan	⊢ ((φ ∧ ψ) ↔ ¬ (φ ⊼ ψ))

Proof of Theorem nanan

Step	Hyp	Ref	Expression
1		df-nan 1288	. 2 ⊢ ((φ ⊼ ψ) ↔ ¬ (φ ∧ ψ))
2	1	con2bii 322	1 ⊢ ((φ ∧ ψ) ↔ ¬ (φ ⊼ ψ))

Syntax hints:  ¬ wn 3   ↔ wb 176   ∧ wa 358   ⊼ wnan 1287

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-nan 1288

This theorem is referenced by: (None)