Theorem norer-P4.2b 370

Description: Negated Right '∨' Elimination. †

Hypothesis

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

Assertion

Ref	Expression
norer-P4.2b	⊢ (𝛾 → ¬ 𝜑)

Proof of Theorem norer-P4.2b

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ 𝜑) → 𝜑)
2	1	ndorir-P3.11 176	. 2 ⊢ ((𝛾 ∧ 𝜑) → (𝜑 ∨ 𝜓))
3		norer-P4.2b.1	. . 3 ⊢ (𝛾 → ¬ (𝜑 ∨ 𝜓))
4	3	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ 𝜑) → ¬ (𝜑 ∨ 𝜓))
5	2, 4	rcp-NDNEGI2 219	1 ⊢ (𝛾 → ¬ 𝜑)

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:  norer-P4.2b.RC  371  norer-P4.2b.CL  372