Theorem ancr 243

Description: Conjoin antecedent to right of consequent.

Assertion

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

Proof of Theorem ancr

Step	Hyp	Ref	Expression
1		pm3.21 233	. 2 ⊢ (φ → (ψ → (ψ ∧ φ)))
2	1	a2i 8	1 ⊢ ((φ → ψ) → (φ → (ψ ∧ φ)))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  ancrd 247  ancrb 265  nnmord 3189  chsscm 5147

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

metamath.org