Theorem alrimdv 1887

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)

Hypothesis

Ref	Expression
alrimdv.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
alrimdv	⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Distinct variable groups:   𝜑,𝑥   𝜓,𝑥

Allowed substitution hint:   𝜒(𝑥)

Proof of Theorem alrimdv

Step	Hyp	Ref	Expression
1		ax-17 1537	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		ax-17 1537	. 2 ⊢ (𝜓 → ∀𝑥𝜓)
3		alrimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 2, 3	alrimdh 1490	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1458  ax-gen 1460  ax-17 1537

This theorem is referenced by:  exmidsssnc  4232  funcnvuni  5323  fliftfun  5839  findcard  6944  findcard2  6945  findcard2s  6946  genprndl  7581  genprndu  7582  seqf1og  10592  bj-inf2vnlem2  15463