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Theorem albid 1506
Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
albid.1 𝑥𝜑
albid.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
albid (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))

Proof of Theorem albid
StepHypRef Expression
1 albid.1 . . 3 𝑥𝜑
21nfri 1412 . 2 (𝜑 → ∀𝑥𝜑)
3 albid.2 . 2 (𝜑 → (𝜓𝜒))
42, 3albidh 1369 1 (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1241  wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  alexdc  1510  19.32dc  1569  eubid  1907  ralbida  2317  raleqf  2498  intab  3641  bdsepnft  9880  strcollnft  9982  sscoll2  9986
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