Theorem bicon1d 405

Description: A contraposition deduction.

Hypothesis

Ref	Expression
bicon1d.1	⊢ (φ → (¬ ψ ↔ χ))

Assertion

Ref	Expression
bicon1d	⊢ (φ → (¬ χ ↔ ψ))

Proof of Theorem bicon1d

Step	Hyp	Ref	Expression
1		bicon1d.1	. . . 4 ⊢ (φ → (¬ ψ ↔ χ))
2	1	bicomd 399	. . 3 ⊢ (φ → (χ ↔ ¬ ψ))
3	2	bicon2d 404	. 2 ⊢ (φ → (ψ ↔ ¬ χ))
4	3	bicomd 399	1 ⊢ (φ → (¬ χ ↔ ψ))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127

This theorem is referenced by:  onmindif 2312  lttri2t 4280  pjelt 5668

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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