Theorem con2b 348

Description: Contraposition. Bidirectional version of con2 129. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
con2b	⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 129	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2		con2 129	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
3	1, 2	impbii 198	1 ⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195

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 196

This theorem is referenced by:  mt2bi  352  pm4.15  603  nic-ax  1589  nic-axALT  1590  alimex  1748  ssconb  3705  disjsn  4192  oneqmini  5693  kmlem4  8858  isprm3  15234  bnj1171  30322  bnj1176  30327  bnj1204  30334  bnj1388  30355  bnj1523  30393  wl-nancom  32476  dfxor5  37078  pm13.196a  37637