Theorem orintl-P2.11a 146

Description: Left Introduction Rule for '∨'.

Assertion

Ref	Expression
orintl-P2.11a	⊢ (𝜑 → (𝜓 ∨ 𝜑))

Proof of Theorem orintl-P2.11a

Step	Hyp	Ref	Expression
1		poe-P1.11b 66	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))
2		trnsp-P1.15b 78	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑))
3		df-or-D2.3 145	. . 3 ⊢ ((𝜓 ∨ 𝜑) ↔ (¬ 𝜓 → 𝜑))
4	3	birev-P2.5b.SH 116	. 2 ⊢ ((¬ 𝜓 → 𝜑) → (𝜓 ∨ 𝜑))
5	1, 2, 4	dsyl-P1.3 35	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑))

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-or-D2.3 145

This theorem is referenced by:  orintl-P2.11a.AC.SH  147  exclmid-P2.12  152