Theorem anim12ii 553

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007.) (Proof shortened by Wolf Lammen, 19-Jul-2013.)

Hypotheses

Ref	Expression
anim12ii.1	⊢ (φ → (ψ → χ))
anim12ii.2	⊢ (θ → (ψ → τ))

Assertion

Ref	Expression
anim12ii	⊢ ((φ ∧ θ) → (ψ → (χ ∧ τ)))

Proof of Theorem anim12ii

Step	Hyp	Ref	Expression
1		anim12ii.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	adantr 451	. 2 ⊢ ((φ ∧ θ) → (ψ → χ))
3		anim12ii.2	. . 3 ⊢ (θ → (ψ → τ))
4	3	adantl 452	. 2 ⊢ ((φ ∧ θ) → (ψ → τ))
5	2, 4	jcad 519	1 ⊢ ((φ ∧ θ) → (ψ → (χ ∧ τ)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

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

This theorem is used by:  euim  2254  elex22  2871  sfinltfin  4536  funcnvuni  5162