Theorem rcp-NDIMI4 226

Description: → Introduction Recipe. †

Hypothesis

Ref	Expression
rcp-NDIMI4.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)

Assertion

Ref	Expression
rcp-NDIMI4	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → (𝛾₄ → 𝜑))

Proof of Theorem rcp-NDIMI4

Step	Hyp	Ref	Expression
1		rcp-NDIMI4.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)
2	1	rcp-NDSEP4 187	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) ∧ 𝛾₄) → 𝜑)
3	2	ndimi-P3.5 170	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → (𝛾₄ → 𝜑))

Syntax hints:   → wff-imp 10   ∧ wff-rcp-AND3 160   ∧ wff-rcp-AND4 162

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-rcp-AND4 163

This theorem is referenced by:  example-E3.1a  309