pm2.45 - Metamath Proof Explorer

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Theorem pm2.45 874

Description: Theorem *2.45 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

**Assertion**
Ref	Expression
pm2.45	⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

**Proof of Theorem pm2.45**
Step	Hyp	Ref	Expression
1		orc 862	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	con3i 157	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

Colors of variables: wff setvar class

Syntax hints: ¬ wn 3 → wi 4 ∨ wo 842

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

This theorem depends on definitions: df-bi 208 df-or 843

This theorem is referenced by: pm2.47 876 dn1 1048 eueq3 3633 outpasch 26211 acopyeu 26291 tgasa1 26315 unbdqndv2lem1 33401