Theorem ancrb 265

Description: Conjoin antecedent to right of consequent.

Assertion

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

Proof of Theorem ancrb

Step	Hyp	Ref	Expression
1		ancr 243	. 2 ⊢ ((φ → ψ) → (φ → (ψ ∧ φ)))
2		pm3.26 256	. . 3 ⊢ ((ψ ∧ φ) → ψ)
3	2	syl3 18	. 2 ⊢ ((φ → (ψ ∧ φ)) → (φ → ψ))
4	1, 3	impbi 139	1 ⊢ ((φ → ψ) ↔ (φ → (ψ ∧ φ)))

Syntax hints:   → wi 2   ↔ wb 127   ∧ wa 196

This theorem is referenced by:  iba 486

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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