Theorem ancr 321

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
ancr	⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

Proof of Theorem ancr

Step	Hyp	Ref	Expression
1		pm3.21 264	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))
2	1	a2i 11	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 104

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

This theorem is referenced by:  bimsc1  965  ssddif  3397  reupick2  3449  intmin4  3902