Theorem mt3d 101

Description: Modus tollens deduction.

Hypotheses

Ref	Expression
mt3d.1	⊢ (φ → ¬ χ)
mt3d.2	⊢ (φ → (¬ ψ → χ))

Assertion

Ref	Expression
mt3d	⊢ (φ → ψ)

Proof of Theorem mt3d

Step	Hyp	Ref	Expression
1		mt3d.1	. 2 ⊢ (φ → ¬ χ)
2		mt3d.2	. . 3 ⊢ (φ → (¬ ψ → χ))
3	2	con1d 85	. 2 ⊢ (φ → (¬ χ → ψ))
4	1, 3	mpd 46	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  ecased 643  nnsuc 2389  sdomdomtr 3370  zbtwnre 4619  atsseq 5745  atom1d 5750

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

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