Theorem 3anim1i 1138

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

Hypothesis

Ref	Expression
3animi.1	⊢ (φ → ψ)

Assertion

Ref	Expression
3anim1i	⊢ ((φ ∧ χ ∧ θ) → (ψ ∧ χ ∧ θ))

Proof of Theorem 3anim1i

Step	Hyp	Ref	Expression
1		3animi.1	. 2 ⊢ (φ → ψ)
2		id 19	. 2 ⊢ (χ → χ)
3		id 19	. 2 ⊢ (θ → θ)
4	1, 2, 3	3anim123i 1137	1 ⊢ ((φ ∧ χ ∧ θ) → (ψ ∧ χ ∧ θ))

This proof depends on syntax axioms:   → wi 4   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by:  syl3an1  1215  syl3anl1  1230  syl3anr1  1234