Theorem imoverim-P4.30a 477

Description: '→' Distributes Over Itself . †

Assertion

Ref	Expression
imoverim-P4.30a	⊢ ((𝜑 → (𝜓 → 𝜒)) ↔ ((𝜑 → 𝜓) → (𝜑 → 𝜒)))

Proof of Theorem imoverim-P4.30a

Step	Hyp	Ref	Expression
1		axL2-P3.22.CL 256	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2		imoverim-P4.30-L1 476	. 2 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) ↔ ((𝜑 → 𝜓) → (𝜑 → 𝜒)))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104

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-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  imoverbi-P4.30b  479