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Theorem ralimia 2436
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 2435 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1438  wral 2359
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383
This theorem depends on definitions:  df-bi 115  df-ral 2364
This theorem is referenced by:  ralimiaa  2437  ralimi  2438  r19.12  2478  rr19.3v  2755  rr19.28v  2756  ffvresb  5461  f1mpt  5550  peano2nnnn  7390  peano5nnnn  7427  peano5nni  8425  peano2nn  8434  serf0  10741
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