Theorem con2b 349

Description: Contraposition. Bidirectional version of con2 130. (Contributed by NM, 12-Mar-1993.)

Assertion

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

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 130	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2		con2 130	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
3	1, 2	impbii 199	1 ⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 196

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 197

This theorem is referenced by:  mt2bi  353  pm4.15  605  nic-ax  1598  nic-axALT  1599  alimex  1758  ssconb  3743  disjsn  4246  oneqmini  5776  kmlem4  8975  isprm3  15396  bnj1171  31068  bnj1176  31073  bnj1204  31080  bnj1388  31101  bnj1523  31139  wl-nancom  33297  dfxor5  38059  pm13.196a  38615