Theorem rcp-NDIMP4add1 211

Description: ( 1 ∧ 2 ∧ 3 ∧ 4 ) ⇒ ( 1 ∧ 2 ∧ 3 ∧ 4 ∧ 5 ). †

Hypothesis

Ref	Expression
rcp-NDIMP4add1.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)

Assertion

Ref	Expression
rcp-NDIMP4add1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → 𝜑)

Proof of Theorem rcp-NDIMP4add1

Step	Hyp	Ref	Expression
1		rcp-NDIMP4add1.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)
2	1	ndimp-P3.2 167	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) ∧ 𝛾₅) → 𝜑)
3	2	rcp-NDJOIN5 191	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → 𝜑)

Syntax hints:   → wff-imp 10   ∧ wff-rcp-AND4 162   ∧ wff-rcp-AND5 164

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-AND5 165

This theorem is referenced by:  rcp-NDIMP3add2  214  rcp-NDIMP2add3  216  rcp-NDIMP1add4  217  example-E3.2b  312