Theorem mt3i 100

Description: Modus tollens inference.

Hypotheses

Ref	Expression
mt3i.1	⊢ ¬ χ
mt3i.2	⊢ (φ → (¬ ψ → χ))

Assertion

Ref	Expression
mt3i	⊢ (φ → ψ)

Proof of Theorem mt3i

Step	Hyp	Ref	Expression
1		mt3i.1	. 2 ⊢ ¬ χ
2		mt3i.2	. . 3 ⊢ (φ → (¬ ψ → χ))
3	2	con1d 85	. 2 ⊢ (φ → (¬ χ → ψ))
4	1, 3	mpi 44	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  a16g 933  ordeleqon 2241  limom 2387  zornlem4 3606  inelr 4527  crulem 4528

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

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