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Theorem stdpc5 1473
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 1587. 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  F/
Assertion
Ref Expression
stdpc5

Proof of Theorem stdpc5
StepHypRef Expression
1 stdpc5.1 . . 3  F/
2119.21 1472 . 2
32biimpi 113 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   F/wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  sbalyz  1872  ra5  2840
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