axfrege28 - Mathbox for Richard Penner

	Mathbox for Richard Penner		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > Mathboxes > axfrege28		Structured version Visualization version GIF version

Theorem axfrege28 41326

Description: Contraposition. Identical to con3 153. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by RP, 24-Dec-2019.)

**Assertion**
Ref	Expression
axfrege28	⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))

**Proof of Theorem axfrege28**
Step	Hyp	Ref	Expression
1		con3 153	1 ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑))

Colors of variables: wff setvar class

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: (None)