Theorem 3anim3i 1177

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)

Hypothesis

Ref	Expression
3animi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3anim3i	⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Proof of Theorem 3anim3i

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜒 → 𝜒)
2		id 19	. 2 ⊢ (𝜃 → 𝜃)
3		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
4	1, 2, 3	3anim123i 1174	1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  syl3anl3  1278  syl3anr3  1282  elioo4g  9870