Theorem nsyl2 103

Description: A negated syllogism inference.

Hypotheses

Ref	Expression
nsyl2.1	⊢ (φ → ¬ ψ)
nsyl2.2	⊢ (¬ χ → ψ)

Assertion

Ref	Expression
nsyl2	⊢ (φ → χ)

Proof of Theorem nsyl2

Step	Hyp	Ref	Expression
1		nsyl2.1	. 2 ⊢ (φ → ¬ ψ)
2		nsyl2.2	. . 3 ⊢ (¬ χ → ψ)
3	2	con1i 88	. 2 ⊢ (¬ ψ → χ)
4	1, 3	syl 12	1 ⊢ (φ → χ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  tfi 2244  peano5 2394  setind 3492  rankel 3524  r1pwcl 3530  alephnbtwn 3674

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

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