Theorem orasim-P3.48a 361

Description: '∨' in Terms of '→'.

This is the re-derived Chapter 2 definition. Only orasimint-P3.48b 362 is deducible with intuitionist logic.

Assertion

Ref	Expression
orasim-P3.48a	⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))

Proof of Theorem orasim-P3.48a

Step	Hyp	Ref	Expression
1		orasim-P3.48-L1 359	. 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))
2		orasim-P3.48-L2 360	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ↔ wff-bi 104   ∨ 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  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  nfrord-P6  817