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Theorem rspec3 2714
Description: Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rspec3.1 x A y B z C φ
Assertion
Ref Expression
rspec3 ((x A y B z C) → φ)

Proof of Theorem rspec3
StepHypRef Expression
1 rspec3.1 . . . 4 x A y B z C φ
21rspec2 2713 . . 3 ((x A y B) → z C φ)
32r19.21bi 2712 . 2 (((x A y B) z C) → φ)
433impa 1146 1 ((x A y B z C) → φ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934   wcel 1710  wral 2614
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-an 360  df-3an 936  df-ex 1542  df-ral 2619
This theorem is referenced by: (None)
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