Theorem joinimandinc2-P4 576

Description: Alternate form of joinimandinc-P4.8a 397. †

Hypotheses

Ref	Expression
joinimandinc2-P4.1	⊢ (𝛾 → (𝜑 → 𝜓))
joinimandinc2-P4.2	⊢ (𝛾 → (𝜒 → 𝜗))

Assertion

Ref	Expression
joinimandinc2-P4	⊢ (𝛾 → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜗)))

Proof of Theorem joinimandinc2-P4

Step	Hyp	Ref	Expression
1		joinimandinc2-P4.1	. . 3 ⊢ (𝛾 → (𝜑 → 𝜓))
2		joinimandinc2-P4.2	. . 3 ⊢ (𝛾 → (𝜒 → 𝜗))
3	1, 2	ndandi-P3.7 172	. 2 ⊢ (𝛾 → ((𝜑 → 𝜓) ∧ (𝜒 → 𝜗)))
4	3	joinimandinc-P4.8a 397	1 ⊢ (𝛾 → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜗)))

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-rcp-AND3 161

This theorem is referenced by:  joinimandinc2-P4.RC  577