Theorem imoveror-P4.29b 474

Description: '→' Left Distributes Over '∨' .

Assertion

Ref	Expression
imoveror-P4.29b	⊢ ((𝜑 → (𝜓 ∨ 𝜒)) ↔ ((𝜑 → 𝜓) ∨ (𝜑 → 𝜒)))

Proof of Theorem imoveror-P4.29b

Step	Hyp	Ref	Expression
1		sepimorr-P4.9c.CL 414	. 2 ⊢ ((𝜑 → (𝜓 ∨ 𝜒)) → ((𝜑 → 𝜓) ∨ (𝜑 → 𝜒)))
2		imoveror-P4.29-L1 473	. 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   ∨ wff-or 144

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-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by: (None)