Theorem atbiffatnnbalt 47711

Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 29-Aug-2016.)

Assertion

Ref	Expression
atbiffatnnbalt	⊢ ((𝜑 → 𝜓) → (𝜑 → ¬ ¬ 𝜓))

Proof of Theorem atbiffatnnbalt

Step	Hyp	Ref	Expression
1		atbiffatnnb 47709	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → ¬ ¬ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

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

This theorem is used by: (None)