Theorem rcp-NDIMP1add2 212

Description: ( 1 ) ⇒ ( 1 ∧ 2 ∧ 3 ). †

Hypothesis

Ref	Expression
rcp-NDIMP1add2.1	⊢ (𝛾₁ → 𝜑)

Assertion

Ref	Expression
rcp-NDIMP1add2	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)

Proof of Theorem rcp-NDIMP1add2

Step	Hyp	Ref	Expression
1		rcp-NDIMP1add2.1	. . 3 ⊢ (𝛾₁ → 𝜑)
2	1	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾₁ ∧ 𝛾₂) → 𝜑)
3	2	rcp-NDIMP2add1 209	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)

Syntax hints:   → wff-imp 10   ∧ 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-NDIMP1add3  215  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  suborl-P3.43a-L1  345  joinimandinc-P4.8a  397  sepimorr-P4.9c  412  sepimandl-P4.9d  415