Metamath Proof Explorer


Theorem anim2i

Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 3-Jan-1993)

Ref Expression
Hypothesis anim1i.1 ⊢ ( 𝜑 → 𝜓 )
Assertion anim2i ( ( 𝜒 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 anim1i.1 ⊢ ( 𝜑 → 𝜓 )
2 id ⊢ ( 𝜒 → 𝜒 )
3 2 1 anim12i ⊢ ( ( 𝜒 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜓 ) )