Theorem ancr 555

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		pm3.21 476	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))
2	1	a2i 15	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  bimsc1  857  reupick2  4292  intmin4  4946  replem  5253  bnj1098  35116  lukshef-ax2  36814  bj-opelid  37687  poimirlem25  38183  pm14.122b  45024