Theorem orassoc2a-P4 572

Description: Alternate Form A of orassoc-P3.38 322. †

Hypothesis

Ref	Expression
orassoc2a-P4.1	⊢ (𝛾 → ((𝜑 ∨ 𝜓) ∨ 𝜒))

Assertion

Ref	Expression
orassoc2a-P4	⊢ (𝛾 → (𝜑 ∨ (𝜓 ∨ 𝜒)))

Proof of Theorem orassoc2a-P4

Step	Hyp	Ref	Expression
1		orassoc2a-P4.1	. 2 ⊢ (𝛾 → ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orassoc-P3.38 322	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	subimr2-P4.RC 543	1 ⊢ (𝛾 → (𝜑 ∨ (𝜓 ∨ 𝜒)))

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-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  orassoc2a-P4.RC  573