Theorem mt4d 115

Description: Modus tollens deduction.

Hypotheses

Ref	Expression
mt4d.1	⊢ (φ → ψ)
mt4d.2	⊢ (φ → (¬ χ → ¬ ψ))

Assertion

Ref	Expression
mt4d	⊢ (φ → χ)

Proof of Theorem mt4d

Step	Hyp	Ref	Expression
1		mt4d.1	. 2 ⊢ (φ → ψ)
2		mt4d.2	. . 3 ⊢ (φ → (¬ χ → ¬ ψ))
3	2	a3d 75	. 2 ⊢ (φ → (ψ → χ))
4	1, 3	mpd 26	1 ⊢ (φ → χ)

Syntax hints:  ¬ wn 2   → wi 3

This theorem is referenced by:  atom1d 10188

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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