Theorem rae-P1.5 37

Description: Redundant Antecedent Elimination.

Assertion

Ref	Expression
rae-P1.5	⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓))

Proof of Theorem rae-P1.5

Step	Hyp	Ref	Expression
1		ax-L2 12	. 2 ⊢ ((𝜑 → (𝜑 → 𝜓)) → ((𝜑 → 𝜑) → (𝜑 → 𝜓)))
2		id-P1.4 36	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	mae-P1.1 33	1 ⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓))

Syntax hints:   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-MP 14

This theorem is referenced by:  rae-P1.5.SH  38