Theorem orintr-P2.11b 148

Description: Right Introduction Rule for '∨'.

Assertion

Ref	Expression
orintr-P2.11b	⊢ (𝜑 → (𝜑 ∨ 𝜓))

Proof of Theorem orintr-P2.11b

Step	Hyp	Ref	Expression
1		poe-P1.11b 66	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))
2		df-or-D2.3 145	. . 3 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	2	birev-P2.5b.SH 116	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓))
4	1, 3	syl-P1.2 34	1 ⊢ (𝜑 → (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-or-D2.3 145

This theorem is referenced by:  orintr-P2.11b.AC.SH  149  exclmid-P2.12  152