Theorem mtbid 536

Description: A deduction from a biconditional, similar to modus tollens.

Hypotheses

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

Assertion

Ref	Expression
mtbid	⊢ (φ → ¬ χ)

Proof of Theorem mtbid

Step	Hyp	Ref	Expression
1		mtbid.min	. 2 ⊢ (φ → ¬ ψ)
2		mtbid.maj	. . 3 ⊢ (φ → (ψ ↔ χ))
3	2	biimprd 136	. 2 ⊢ (φ → (χ → ψ))
4	1, 3	mtod 95	1 ⊢ (φ → ¬ χ)

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

This theorem is referenced by:  axpownd 3747  genpnnp 3902

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

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