Theorem nsyl4 105

Description: A negated syllogism inference.

Hypotheses

Ref	Expression
nsyl4.1	⊢ (φ → ψ)
nsyl4.2	⊢ (¬ φ → χ)

Assertion

Ref	Expression
nsyl4	⊢ (¬ χ → ψ)

Proof of Theorem nsyl4

Step	Hyp	Ref	Expression
1		nsyl4.2	. . 3 ⊢ (¬ φ → χ)
2	1	con1i 88	. 2 ⊢ (¬ χ → φ)
3		nsyl4.1	. 2 ⊢ (φ → ψ)
4	2, 3	syl 12	1 ⊢ (¬ χ → ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  pm5.18 497  hbne 699  eq4ds 823  tz6.12i 2847  eceqopreq 3249

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

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