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Theorem stdpc7 1891
 Description: One of the two equality axioms of standard predicate calculus, called substitutivity of equality. (The other one is stdpc6 1821.) Translated to traditional notation, it can be read: " , provided that is free for in ." Axiom 7 of [Mendelson] p. 95. (Contributed by NM, 15-Feb-2005.)
Assertion
Ref Expression
stdpc7

Proof of Theorem stdpc7
StepHypRef Expression
1 sbequ2 1890 . 2
21equcoms 1825 1
 Colors of variables: wff set class Syntax hints:   wi 6  wsb 1882 This theorem is referenced by:  ax16  1925  sbequi  1951  sb5rf  1984  sb8  1986 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540  df-sb 1883
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