Theorem rcp-IMPIME2 528

Description: '→' Elimination with Importation. †

Hypothesis

Ref	Expression
rcp-IMPIME2.1	⊢ ((𝛾₁ ∧ 𝛾₂) → (𝜑 → 𝜓))

Assertion

Ref	Expression
rcp-IMPIME2	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝜑) → 𝜓)

Proof of Theorem rcp-IMPIME2

Step	Hyp	Ref	Expression
1		rcp-IMPIME2.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂) → (𝜑 → 𝜓))
2	1	impime-P4 526	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝜑) → 𝜓)
3	2	rcp-NDJOIN3 189	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝜑) → 𝜓)

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:  psubaddv-P6-L1  807  psubmultv-P6-L1  809