Theorem rae-P3.26 263

Description: Redundant Antecedent Elimination. †

Hypothesis

Ref	Expression
rae-P3.26.1	⊢ (𝛾 → (𝜑 → (𝜑 → 𝜓)))

Assertion

Ref	Expression
rae-P3.26	⊢ (𝛾 → (𝜑 → 𝜓))

Proof of Theorem rae-P3.26

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ 𝜑) → 𝜑)
2		rae-P3.26.1	. . . . 5 ⊢ (𝛾 → (𝜑 → (𝜑 → 𝜓)))
3	2	rcp-NDIMP1add1 208	. . . 4 ⊢ ((𝛾 ∧ 𝜑) → (𝜑 → (𝜑 → 𝜓)))
4	1, 3	ndime-P3.6 171	. . 3 ⊢ ((𝛾 ∧ 𝜑) → (𝜑 → 𝜓))
5	1, 4	ndime-P3.6 171	. 2 ⊢ ((𝛾 ∧ 𝜑) → 𝜓)
6	5	rcp-NDIMI2 224	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:  rae-P3.26.RC  264