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Theorem alrimd 1603
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimd.1 𝑥𝜑
alrimd.2 𝑥𝜓
alrimd.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimd (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimd
StepHypRef Expression
1 alrimd.1 . 2 𝑥𝜑
2 alrimd.2 . . 3 𝑥𝜓
32a1i 9 . 2 (𝜑 → Ⅎ𝑥𝜓)
4 alrimd.3 . 2 (𝜑 → (𝜓𝜒))
51, 3, 4alrimdd 1602 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1346  wnf 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1440  ax-gen 1442  ax-4 1503
This theorem depends on definitions:  df-bi 116  df-nf 1454
This theorem is referenced by:  euexex  2104  ralrimd  2548  fiintim  6904
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