Theorem anim12d1 622

Description: Variant of anim12d 621 where the second implication does not depend on the antecedent. (Contributed by Rodolfo Medina, 12-Oct-2010.)

Hypotheses

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

Assertion

Ref	Expression
anim12d1	⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜏)))

Proof of Theorem anim12d1

Step	Hyp	Ref	Expression
1		anim12d1.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		anim12d1.2	. . 3 ⊢ (𝜃 → 𝜏)
3	2	a1i 11	. 2 ⊢ (𝜑 → (𝜃 → 𝜏))
4	1, 3	anim12d 621	1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜏)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  fun  6736  frrlem13  8300  alephord  10135  grudomon  10883  xrsupexmnf  13416  xrinfmexpnf  13417  joinfval  18525  meetfval  18539  cnpresti  23586  1stcrest  23751  upgrwlkdvdelem  30304