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Theorem ra5 3130
Description: Restricted quantifier version of Axiom 5 of [Mendelson] p. 69. This is an axiom of a predicate calculus for a restricted domain. Compare the unrestricted stdpc5 1798. (Contributed by NM, 16-Jan-2004.)
Hypothesis
Ref Expression
ra5.1  F/
Assertion
Ref Expression
ra5

Proof of Theorem ra5
StepHypRef Expression
1 df-ral 2619 . . . 4
2 bi2.04 350 . . . . 5
32albii 1566 . . . 4
41, 3bitri 240 . . 3
5 ra5.1 . . . 4  F/
65stdpc5 1798 . . 3
74, 6sylbi 187 . 2
8 df-ral 2619 . 2
97, 8syl6ibr 218 1
Colors of variables: wff setvar class
Syntax hints:   wi 4  wal 1540   F/wnf 1544   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2619
This theorem is referenced by: (None)
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