Theorem rcp-NDASM2of3 196

Description: ( 1 ∧ 2 ∧ 3 ) → 2. †

Assertion

Ref	Expression
rcp-NDASM2of3	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝛾₂)

Proof of Theorem rcp-NDASM2of3

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂) → 𝛾₂)
2	1	ndimp-P3.2 167	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝛾₃) → 𝛾₂)
3	2	rcp-NDJOIN3 189	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝛾₂)

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-NDASM2of4  199  ndnegi-P3.3.CL  242  axL2-P3.22  254  imcomm-P3.27  265  trnsp-P3.31a  279  trnsp-P3.31b  282  trnsp-P3.31c  285  trnsp-P3.31d  288  export-P3.34b  307  orasim-P3.48-L1  359  joinimor-P4.8c  403  sepimorr-P4.9c  412  sepimandl-P4.9d  415  oroverand-P4.27-L4  463  oroverim-P4.28-L2  466  psubaddv-P6-L1  807  psubmultv-P6-L1  809  qimeqex-P7-L2  1055