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Theorem albid 1772
 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 1762 . 2 (φxφ)
3 albid.2 . 2 (φ → (ψχ))
42, 3albidh 1590 1 (φ → (xψxχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  nfbidf  1774  ax11v2  1992  sbcom  2089  sbal2  2134  ax11eq  2193  ax11el  2194  ax11v2-o  2201  eubid  2211  ralbida  2628  raleqf  2803  intab  3956
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