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Theorem ralimia 2518
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996.)
Hypothesis
Ref Expression
ralimia.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
ralimia (∀𝑥𝐴 𝜑 → ∀𝑥𝐴 𝜓)

Proof of Theorem ralimia
StepHypRef Expression
1 ralimia.1 . . 3 (𝑥𝐴 → (𝜑𝜓))
21a2i 11 . 2 ((𝑥𝐴𝜑) → (𝑥𝐴𝜓))
32ralimi2 2517 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2128  wral 2435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429
This theorem depends on definitions:  df-bi 116  df-ral 2440
This theorem is referenced by:  ralimiaa  2519  ralimi  2520  r19.12  2563  rr19.3v  2851  rr19.28v  2852  ffvresb  5630  f1mpt  5721  ixpf  6665  exmidontri2or  7178  peano2nnnn  7773  peano5nnnn  7812  peano5nni  8836  peano2nn  8845  serf0  11249  baspartn  12459  tridceq  13638
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