Theorem orintr-P2.11b.AC.SH 149

Description: Deductive Form of orintr-P2.11b 148.

Hypothesis

Ref	Expression
orintr-P2.11b.AC.SH.1	⊢ (𝛾 → 𝜑)

Assertion

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

Proof of Theorem orintr-P2.11b.AC.SH

Step	Hyp	Ref	Expression
1		orintr-P2.11b.AC.SH.1	. 2 ⊢ (𝛾 → 𝜑)
2		orintr-P2.11b 148	. . . 4 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → (𝜑 → (𝜑 ∨ 𝜓)))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → 𝜑) → (𝛾 → (𝜑 ∨ 𝜓)))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → (𝜑 ∨ 𝜓))

Syntax hints:   → 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:  ndorir-P3.11  176