Theorem joinimor3-P4 586

Description: Alternate form of joinimor-P4.8c 403. †

Hypothesis

Ref	Expression
joinimor3-P4.1	⊢ (𝛾 → ((𝜑 → 𝜓) ∨ (𝜑 → 𝜒)))

Assertion

Ref	Expression
joinimor3-P4	⊢ (𝛾 → (𝜑 → (𝜓 ∨ 𝜒)))

Proof of Theorem joinimor3-P4

Step	Hyp	Ref	Expression
1		joinimor3-P4.1	. . 3 ⊢ (𝛾 → ((𝜑 → 𝜓) ∨ (𝜑 → 𝜒)))
2	1	joinimor-P4.8c 403	. 2 ⊢ (𝛾 → ((𝜑 ∧ 𝜑) → (𝜓 ∨ 𝜒)))
3		idempotand-P4.25a 450	. . 3 ⊢ ((𝜑 ∧ 𝜑) ↔ 𝜑)
4	3	rcp-NDIMP0addall 207	. 2 ⊢ (𝛾 → ((𝜑 ∧ 𝜑) ↔ 𝜑))
5	2, 4	subiml2-P4 540	1 ⊢ (𝛾 → (𝜑 → (𝜓 ∨ 𝜒)))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104   ∧ wff-and 132   ∨ 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:  joinimor3-P4.RC  587