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Theorem anclb 530

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 490	. 2 ⊢ (φ → (ψ ↔ (φ ∧ ψ)))
2	1	pm5.74i 236	1 ⊢ ((φ → ψ) ↔ (φ → (φ ∧ ψ)))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360

This theorem is referenced by: pm4.71 611 difin 3492

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