This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem anim12d1

Description: Variant of anim12d where the second implication does not depend on the antecedent. (Contributed by Rodolfo Medina, 12-Oct-2010)

Ref Expression
Hypotheses anim12d1.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
anim12d1.2 ⊢ ( 𝜃 → 𝜏 )
Assertion anim12d1 ( 𝜑 → ( ( 𝜓 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜏 ) ) )

Proof

Step Hyp Ref Expression
1 anim12d1.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2 anim12d1.2 ⊢ ( 𝜃 → 𝜏 )
3 2 a1i ⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
4 1 3 anim12d ⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜏 ) ) )