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Theorem albid 1503
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 → (xψxχ))

Proof of Theorem albid
StepHypRef Expression
1 albid.1 . . 3 xφ
21nfri 1409 . 2 (φxφ)
3 albid.2 . 2 (φ → (ψχ))
42, 3albidh 1366 1 (φ → (xψxχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240  wnf 1346
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 1333  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  alexdc  1507  19.32dc  1566  eubid  1904  ralbida  2314  raleqf  2495  intab  3635  bdsepnft  9321  strcollnft  9414  sscoll2  9418
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