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Theorem 2albidv 1627
Description: Formula-building rule for 2 universal quantifiers (deduction rule). (Contributed by NM, 4-Mar-1997.)
Hypothesis
Ref Expression
2albidv.1 (φ → (ψχ))
Assertion
Ref Expression
2albidv (φ → (xyψxyχ))
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem 2albidv
StepHypRef Expression
1 2albidv.1 . . 3 (φ → (ψχ))
21albidv 1625 . 2 (φ → (yψyχ))
32albidv 1625 1 (φ → (xyψxyχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540
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
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  2mo  2282  2eu6  2289  nnsucelr  4428  ssfin  4470  ncfinlower  4483  dff13  5471  fnfrec  6320
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