Theorem impime-P4 526

Description: '→' Elimination with Importation. †

Hypothesis

Ref	Expression
impime-P4.1	⊢ (𝛾 → (𝜑 → 𝜓))

Assertion

Ref	Expression
impime-P4	⊢ ((𝛾 ∧ 𝜑) → 𝜓)

Proof of Theorem impime-P4

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. 2 ⊢ ((𝛾 ∧ 𝜑) → 𝜑)
2		impime-P4.1	. . 3 ⊢ (𝛾 → (𝜑 → 𝜓))
3	2	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ 𝜑) → (𝜑 → 𝜓))
4	1, 3	ndime-P3.6 171	1 ⊢ ((𝛾 ∧ 𝜑) → 𝜓)

Syntax hints:   → wff-imp 10   ∧ wff-and 132

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

This theorem is referenced by:  rcp-IMPIME1  527  rcp-IMPIME2  528  rcp-IMPIME3  529  rcp-IMPIME4  530