Theorem rimoverandint-P4.31c 483

Description: One Direction of '→' is Antidistributive on the Right Over '∧' . †

Only this direction is deducible with intuitionist logic.

Assertion

Ref	Expression
rimoverandint-P4.31c	⊢ (((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem rimoverandint-P4.31c

Step	Hyp	Ref	Expression
1		rimoverand-P4.31-L1 480	1 ⊢ (((𝜑 → 𝜒) ∨ (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))

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