Theorem bj-con2com 34741

Description: A commuted form of the contrapositive, true in minimal calculus. (Contributed by BJ, 19-Mar-2020.)

Assertion

Ref	Expression
bj-con2com	⊢ (𝜑 → ((𝜓 → ¬ 𝜑) → ¬ 𝜓))

Proof of Theorem bj-con2com

Step	Hyp	Ref	Expression
1		con2 135	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
2	1	com12 32	1 ⊢ (𝜑 → ((𝜓 → ¬ 𝜑) → ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bj-con2comi  34742