Theorem rcp-NDIMI3 225

Description: → Introduction Recipe. †

Hypothesis

Ref	Expression
rcp-NDIMI3.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)

Assertion

Ref	Expression
rcp-NDIMI3	⊢ ((𝛾₁ ∧ 𝛾₂) → (𝛾₃ → 𝜑))

Proof of Theorem rcp-NDIMI3

Step	Hyp	Ref	Expression
1		rcp-NDIMI3.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → 𝜑)
2	1	rcp-NDSEP3 186	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝛾₃) → 𝜑)
3	2	ndimi-P3.5 170	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:  axL2-P3.22  254  imcomm-P3.27  265  export-P3.34b  307  example-E3.1a  309  sepimorr-P4.9c  412  sepimandl-P4.9d  415  oroverim-P4.28-L2  466  psubaddv-P6-L1  807  psubmultv-P6-L1  809  qimeqex-P7-L2  1055