Theorem con1b 361

Description: Contraposition. Bidirectional version of con1 147. (Contributed by NM, 3-Jan-1993.)

Assertion

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

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 147	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑))
2		con1 147	. 2 ⊢ ((¬ 𝜓 → 𝜑) → (¬ 𝜑 → 𝜓))
3	1, 2	impbii 212	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (¬ 𝜓 → 𝜑))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209

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:  eximal  1815  r19.23v  3190  pwssun  5543  ist1-2  23645  cmpfi  23706  dchrelbas2  27546