Theorem lemma-L4.5 484

Description: Lemma 4.5.

Assertion

Ref	Expression
lemma-L4.5	⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Proof of Theorem lemma-L4.5

Step	Hyp	Ref	Expression
1		dmorgb-P4.26b 457	. 2 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜓))
2		dnegeq-P4.10 418	. . 3 ⊢ (¬ ¬ 𝜓 ↔ 𝜓)
3	2	suborr-P3.43b.RC 349	. 2 ⊢ ((¬ 𝜑 ∨ ¬ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
4	1, 3	bitrns-P3.33c.RC 303	1 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Syntax hints:  ¬ wff-neg 9   ↔ wff-bi 104   ∧ 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:  imasand-P4.33a  489