Theorem rcp-NDIMP2add1 209

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

Hypothesis

Ref	Expression
rcp-NDIMP2add1.1	⊢ ((𝛾₁ ∧ 𝛾₂) → 𝜑)

Assertion

Ref	Expression
rcp-NDIMP2add1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)

Proof of Theorem rcp-NDIMP2add1

Step	Hyp	Ref	Expression
1		rcp-NDIMP2add1.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂) → 𝜑)
2	1	ndimp-P3.2 167	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝛾₃) → 𝜑)
3	2	rcp-NDJOIN3 189	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)

Syntax hints:   → wff-imp 10   ∧ wff-and 132   ∧ wff-rcp-AND3 160

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-AND3 161

This theorem is referenced by:  rcp-NDIMP1add2  212  rcp-NDIMP2add2  213  example-E3.2b  312