Theorem rcp-NDASM1of3 195

Description: ( 1 ∧ 2 ∧ 3 ) → 1. †

Assertion

Ref	Expression
rcp-NDASM1of3	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝛾₁)

Proof of Theorem rcp-NDASM1of3

Step	Hyp	Ref	Expression
1		rcp-NDASM1of2 193	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂) → 𝛾₁)
2	1	ndimp-P3.2 167	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝛾₃) → 𝛾₁)
3	2	rcp-NDJOIN3 189	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝛾₁)

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-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  rcp-NDASM1of4  198  ndnegi-P3.3.CL  242  dmorgarev-L4.2  453  andoveror-P4.27-L1  459  oroverim-P4.28-L2  466  psubaddv-P6-L1  807  psubmultv-P6-L1  809