Theorem rcp-RAA1 515

Description: Reductio ad Absurdum.

Hypotheses

Ref	Expression
rcp-RAA1.1	⊢ (¬ 𝛾₁ → 𝜑)
rcp-RAA1.2	⊢ (¬ 𝛾₁ → ¬ 𝜑)

Assertion

Ref	Expression
rcp-RAA1	⊢ 𝛾₁

Proof of Theorem rcp-RAA1

Step	Hyp	Ref	Expression
1		rcp-RAA1.1	. . 3 ⊢ (¬ 𝛾₁ → 𝜑)
2		rcp-RAA1.2	. . 3 ⊢ (¬ 𝛾₁ → ¬ 𝜑)
3	1, 2	rcp-NDNEGI1 218	. 2 ⊢ ¬ ¬ 𝛾₁
4	3	dnege-P3.30.RC 277	1 ⊢ 𝛾₁

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

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  df-true-D2.4 155

This theorem is referenced by: (None)