Theorem pm5.1 601

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		pm5.501 244	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 ↔ 𝜓)))
2	1	biimpa 296	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ↔ 𝜓))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.35  917  ssconb  3270