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Metamath Proof Explorer

Theorem anim12i

Description: Conjoin antecedents and consequents of two premises. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 14-Dec-2013)

Ref Expression
Hypotheses anim12i.1 ⊢ ( 𝜑 → 𝜓 )
anim12i.2 ⊢ ( 𝜒 → 𝜃 )
Assertion anim12i ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) )

Proof

Step Hyp Ref Expression
1 anim12i.1 ⊢ ( 𝜑 → 𝜓 )
2 anim12i.2 ⊢ ( 𝜒 → 𝜃 )
3 id ⊢ ( ( 𝜓 ∧ 𝜃 ) → ( 𝜓 ∧ 𝜃 ) )
4 1 2 3 syl2an ⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) )