Theorem ancrb 533

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

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

Proof of Theorem ancrb

Step	Hyp	Ref	Expression
1		iba 489	. 2 ⊢ (φ → (ψ ↔ (ψ ∧ φ)))
2	1	pm5.74i 236	1 ⊢ ((φ → ψ) ↔ (φ → (ψ ∧ φ)))

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

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

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

This theorem is referenced by: (None)