Theorem con1b 359

Description: Contraposition. Bidirectional version of con1 146. (Contributed by NM, 3-Jan-1993.)

Assertion

Ref	Expression
con1b	⊢ ((¬ 𝜑 → 𝜓) ↔ (¬ 𝜓 → 𝜑))

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 146	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑))
2		con1 146	. 2 ⊢ ((¬ 𝜓 → 𝜑) → (¬ 𝜑 → 𝜓))
3	1, 2	impbii 208	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (¬ 𝜓 → 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205

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 206

This theorem is referenced by:  eximal  1785  r19.23v  3208  pwssun  5485  ist1-2  22498  cmpfi  22559  dchrelbas2  26385