Theorem con1bid 320

Description: A contraposition deduction. (Contributed by NM, 9-Oct-1999.)

Hypothesis

Ref	Expression
con1bid.1	⊢ (φ → (¬ ψ ↔ χ))

Assertion

Ref	Expression
con1bid	⊢ (φ → (¬ χ ↔ ψ))

Proof of Theorem con1bid

Step	Hyp	Ref	Expression
1		con1bid.1	. . . 4 ⊢ (φ → (¬ ψ ↔ χ))
2	1	bicomd 192	. . 3 ⊢ (φ → (χ ↔ ¬ ψ))
3	2	con2bid 319	. 2 ⊢ (φ → (ψ ↔ ¬ χ))
4	3	bicomd 192	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:  pm5.18  345  necon1abid  2570  necon1bbid  2571  opkelimagekg  4272