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Theorem stdpc7 1938
 Description: One of the two equality axioms of standard predicate calculus, called substitutivity of equality. (The other one is stdpc6 1695.) 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 1657 . 2
21equcoms 1689 1
 Colors of variables: wff set class Syntax hints:   wi 4  wsb 1655 This theorem is referenced by:  ax16ALT2  2095  sbequi  2106  sb5rf  2137  sbequiNEW7  28930  sb5rfNEW7  28940  sb8wAUX7  28942  ax16ALT2OLD7  29075  sb8OLD7  29088 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656
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