Theorem pm5.1 590

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)

Assertion

Ref	Expression
pm5.1	⊢ ((𝜑 ∧ 𝜓) → (𝜑 ↔ 𝜓))

Proof of Theorem pm5.1

Step	Hyp	Ref	Expression
1		pm5.501 243	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 ↔ 𝜓)))
2	1	biimpa 294	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ↔ 𝜓))

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.35  902  ssconb  3209