Theorem orasimint-P3.48b 362

Description: Necessary Condition for (i.e. "If" part of) '∨' Defined in Terms of '→' and '¬'. †

Only this direction is deducible with intuitionist logic.

Assertion

Ref	Expression
orasimint-P3.48b	⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))

Proof of Theorem orasimint-P3.48b

Step	Hyp	Ref	Expression
1		orasim-P3.48-L1 359	1 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∨ 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: (None)