Theorem anim12ii 343

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 276	. 2 ⊢ ((𝜑 ∧ 𝜃) → (𝜓 → 𝜒))
3		anim12ii.2	. . 3 ⊢ (𝜃 → (𝜓 → 𝜏))
4	3	adantl 277	. 2 ⊢ ((𝜑 ∧ 𝜃) → (𝜓 → 𝜏))
5	2, 4	jcad 307	1 ⊢ ((𝜑 ∧ 𝜃) → (𝜓 → (𝜒 ∧ 𝜏)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  euim  2113  elex22  2778  tz7.2  4390  funcnvuni  5328  bj-findis  15709