Theorem rcp-FALSERAA2-P 522

Description: Reductio ad Absurdum Using '⊥'.

Hypothesis

Ref	Expression
rcp-FALSERAA2.1	⊢ ((𝛾₁ ∧ ¬ 𝛾₂) → ⊥)

Assertion

Ref	Expression
rcp-FALSERAA2-P	⊢ (𝛾₁ → 𝛾₂)

Proof of Theorem rcp-FALSERAA2-P

Step	Hyp	Ref	Expression
1		rcp-FALSERAA2.1	. . 3 ⊢ ((𝛾₁ ∧ ¬ 𝛾₂) → ⊥)
2	1	rcp-FALSENEGI2 434	. 2 ⊢ (𝛾₁ → ¬ ¬ 𝛾₂)
3	2	dnege-P3.30 276	1 ⊢ (𝛾₁ → 𝛾₂)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132  ⊥wff-false 157

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  df-false-D2.5 158

This theorem is referenced by: (None)