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Theorem stdpc5 1798
Description: An axiom scheme of standard predicate calculus that emulates Axiom 5 of [Mendelson] p. 69. The hypothesis  F/ 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 1678. 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.)
Ref Expression
stdpc5.1  F/
Ref Expression

Proof of Theorem stdpc5
StepHypRef Expression
1 stdpc5.1 . . 3  F/
2119.21 1796 . 2
32biimpi 186 1
Colors of variables: wff setvar class
Syntax hints:   wi 4  wal 1540   F/wnf 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-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  ra5  3130
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