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Theorem alrimdv 1770
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)
Hypothesis
Ref Expression
alrimdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimdv (𝜑 → (𝜓 → ∀𝑥𝜒))
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜒(𝑥)

Proof of Theorem alrimdv
StepHypRef Expression
1 ax-17 1433 . 2 (𝜑 → ∀𝑥𝜑)
2 ax-17 1433 . 2 (𝜓 → ∀𝑥𝜓)
3 alrimdv.1 . 2 (𝜑 → (𝜓𝜒))
41, 2, 3alrimdh 1382 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1350  ax-gen 1352  ax-17 1433
This theorem is referenced by:  funcnvuni  4993  fliftfun  5461  findcard  6373  findcard2  6374  findcard2s  6375  genprndl  6647  genprndu  6648  bj-inf2vnlem2  10426
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