Theorem pm2.01d 81

Description: Deduction based on reductio ad absurdum.

Hypothesis

Ref	Expression
pm2.01d.1	⊢ (φ → (ψ → ¬ ψ))

Assertion

Ref	Expression
pm2.01d	⊢ (φ → ¬ ψ)

Proof of Theorem pm2.01d

Step	Hyp	Ref	Expression
1		pm2.01d.1	. 2 ⊢ (φ → (ψ → ¬ ψ))
2		pm2.01 80	. 2 ⊢ ((ψ → ¬ ψ) → ¬ ψ)
3	1, 2	syl 12	1 ⊢ (φ → ¬ ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  pclem6 555  efrirr 2180  oalimcl 3162  cvnreft 5723

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

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