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Metamath Proof Explorer

Theorem 3anim1i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009)

Ref Expression
Hypothesis 3animi.1 ⊢ ( 𝜑 → 𝜓 )
Assertion 3anim1i ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )

Proof

Step Hyp Ref Expression
1 3animi.1 ⊢ ( 𝜑 → 𝜓 )
2 id ⊢ ( 𝜒 → 𝜒 )
3 id ⊢ ( 𝜃 → 𝜃 )
4 1 2 3 3anim123i ⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )