Theorem anclb 555

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
anclb	⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜑 ∧ 𝜓)))

Proof of Theorem anclb

Step	Hyp	Ref	Expression
1		ibar 538	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 ∧ 𝜓)))
2	1	pm5.74i 274	1 ⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜑 ∧ 𝜓)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  pm4.71  567  difin  4217  bnj1021  35596  dihglblem6  42398  mnuunid  45261