Theorem mtand 591

Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)

Hypotheses

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

Assertion

Ref	Expression
mtand	⊢ (𝜑 → ¬ 𝜓)

Proof of Theorem mtand

Step	Hyp	Ref	Expression
1		mtand.1	. 2 ⊢ (𝜑 → ¬ 𝜒)
2		mtand.2	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
3	2	ex 108	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 3	mtod 589	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem is referenced by:  frirrg  4087  phpm  6327  diffisn  6350  addcanprleml  6712  addcanprlemu  6713