Theorem con2bid 319

Description: A contraposition deduction. (Contributed by NM, 15-Apr-1995.)

Hypothesis

Ref	Expression
con2bid.1	⊢ (φ → (ψ ↔ ¬ χ))

Assertion

Ref	Expression
con2bid	⊢ (φ → (χ ↔ ¬ ψ))

Proof of Theorem con2bid

Step	Hyp	Ref	Expression
1		con2bid.1	. 2 ⊢ (φ → (ψ ↔ ¬ χ))
2		con2bi 318	. 2 ⊢ ((χ ↔ ¬ ψ) ↔ (ψ ↔ ¬ χ))
3	1, 2	sylibr 203	1 ⊢ (φ → (χ ↔ ¬ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176

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 177

This theorem is referenced by:  con1bid  320  necon2abid  2574  necon2bbid  2575  r19.9rzv  3645  iotanul  4355