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Theorem albid 1484
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 1389 . 2 (φxφ)
3 albid.2 . 2 (φ → (ψχ))
42, 3albidh 1345 1 (φ → (xψxχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1224  wnf 1325
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 1312  ax-gen 1314  ax-4 1377
This theorem depends on definitions:  df-bi 110  df-nf 1326
This theorem is referenced by:  alexdc  1488  19.32dc  1547  eubid  1885  ralbida  2294  raleqf  2475  intab  3614  bdsepnft  7305  strcollnft  7398  sscoll2  7402
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