Theorem joinimor2-P4 584

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

Hypothesis

Ref	Expression
joinimor2-P4.1	⊢ (𝛾 → ((𝜑 → 𝜓) ∨ (𝜒 → 𝜓)))

Assertion

Ref	Expression
joinimor2-P4	⊢ (𝛾 → ((𝜑 ∧ 𝜒) → 𝜓))

Proof of Theorem joinimor2-P4

Step	Hyp	Ref	Expression
1		joinimor2-P4.1	. . 3 ⊢ (𝛾 → ((𝜑 → 𝜓) ∨ (𝜒 → 𝜓)))
2	1	joinimor-P4.8c 403	. 2 ⊢ (𝛾 → ((𝜑 ∧ 𝜒) → (𝜓 ∨ 𝜓)))
3		idempotor-P4.25b 451	. . 3 ⊢ ((𝜓 ∨ 𝜓) ↔ 𝜓)
4	3	rcp-NDIMP0addall 207	. 2 ⊢ (𝛾 → ((𝜓 ∨ 𝜓) ↔ 𝜓))
5	2, 4	subimr2-P4 542	1 ⊢ (𝛾 → ((𝜑 ∧ 𝜒) → 𝜓))

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:  joinimor2-P4.RC  585