Theorem ancr 532

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		pm3.21 435	. 2 ⊢ (φ → (ψ → (ψ ∧ φ)))
2	1	a2i 12	1 ⊢ ((φ → ψ) → (φ → (ψ ∧ φ)))

Syntax hints:   → wi 4   ∧ 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:  bimsc1  904  reupick2  3541  intmin4  3955