Theorem norel-P4.2a 367

Description: Negated Left '∨' Elimination. †

Hypothesis

Ref	Expression
norel-P4.2a.1	⊢ (𝛾 → ¬ (𝜑 ∨ 𝜓))

Assertion

Ref	Expression
norel-P4.2a	⊢ (𝛾 → ¬ 𝜓)

Proof of Theorem norel-P4.2a

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ 𝜓) → 𝜓)
2	1	ndoril-P3.10 175	. 2 ⊢ ((𝛾 ∧ 𝜓) → (𝜑 ∨ 𝜓))
3		norel-P4.2a.1	. . 3 ⊢ (𝛾 → ¬ (𝜑 ∨ 𝜓))
4	3	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ 𝜓) → ¬ (𝜑 ∨ 𝜓))
5	2, 4	rcp-NDNEGI2 219	1 ⊢ (𝛾 → ¬ 𝜓)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145

This theorem is referenced by:  norel-P4.2a.RC  368  norel-P4.2a.CL  369