Theorem rcp-NDASM3of4 200

Description: ( 1 ∧ 2 ∧ 3 ∧ 4 ) → 3. †

Assertion

Ref	Expression
rcp-NDASM3of4	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝛾₃)

Proof of Theorem rcp-NDASM3of4

Step	Hyp	Ref	Expression
1		rcp-NDASM3of3 197	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝛾₃)
2	1	ndimp-P3.2 167	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) ∧ 𝛾₄) → 𝛾₃)
3	2	rcp-NDJOIN4 190	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝛾₃)

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-AND3 161  df-rcp-AND4 163

This theorem is referenced by:  rcp-NDASM3of5  204  oroverand-P4.27-L4  463