Theorem mtbii 293

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995.)

Hypotheses

Ref	Expression
mtbii.min	⊢ ¬ ψ
mtbii.maj	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
mtbii	⊢ (φ → ¬ χ)

Proof of Theorem mtbii

Step	Hyp	Ref	Expression
1		mtbii.min	. 2 ⊢ ¬ ψ
2		mtbii.maj	. . 3 ⊢ (φ → (ψ ↔ χ))
3	2	biimprd 214	. 2 ⊢ (φ → (χ → ψ))
4	1, 3	mtoi 169	1 ⊢ (φ → ¬ χ)

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:  ax9  1949