Theorem imasand-P4.33a 489

Description: '→' in Terms of '∧'.

Assertion

Ref	Expression
imasand-P4.33a	⊢ ((𝜑 → 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem imasand-P4.33a

Step	Hyp	Ref	Expression
1		imasor-P4.32a 487	. 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
2		lemma-L4.5 484	. . 3 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
3	2	bisym-P3.33b.RC 299	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))
4	1, 3	bitrns-P3.33c.RC 303	1 ⊢ ((𝜑 → 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ↔ 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: (None)