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Theorem stdpc5 1816
 Description: An axiom scheme of standard predicate calculus that emulates Axiom 5 of [Mendelson] p. 69. The hypothesis can be thought of as emulating " is not free in ." With this definition, the meaning of "not free" is less restrictive than the usual textbook definition; for example would not (for us) be free in by nfequid 1690. This theorem scheme can be proved as a metatheorem of Mendelson's axiom system, even though it is slightly stronger than his Axiom 5. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypothesis
Ref Expression
stdpc5.1
Assertion
Ref Expression
stdpc5

Proof of Theorem stdpc5
StepHypRef Expression
1 stdpc5.1 . . 3
2119.21 1814 . 2
32biimpi 187 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wnf 1553 This theorem is referenced by:  ra5  3245  ax10ext  27583 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
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