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Theorem stdpc7 1801
Description: One of the two equality axioms of standard predicate calculus, called substitutivity of equality. (The other one is stdpc6 1800.) Translated to traditional notation, it can be read: "x= ->( (x,x)-> (x, )), provided that is free for in (x,x)." Axiom 7 of [Mendelson] p. 95. (Contributed by NM, 15-Feb-2005.)
Assertion
Ref Expression
stdpc7

Proof of Theorem stdpc7
StepHypRef Expression
1 sbequ2 1741 . 2
21equcoms 1795 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  [wsb 1739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-sb 1740
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