Theorem alrimdv 1929

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 1579	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		ax-17 1579	. 2 ⊢ (𝜓 → ∀𝑥𝜓)
3		alrimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	1, 2, 3	alrimdh 1532	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

This proof depends on syntax axioms:   → wi 4  ∀wal 1400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1500  ax-gen 1502  ax-17 1579

This theorem is used by:  exmidsssnc  4340  funcnvuni  5450  fliftfun  6002  findcard  7192  findcard2  7193  findcard2s  7194  genprndl  7888  genprndu  7889  seqf1og  10958  bj-inf2vnlem2  16997