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Description: One of the two equality axioms of standard predicate calculus, called substitutivity of equality. (The other one is stdpc6 1631.) 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.) |
Ref | Expression |
---|---|
stdpc7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbequ2 1692 | . 2 | |
2 | 1 | equcoms 1634 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wsb 1685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-gen 1378 ax-ie2 1423 ax-8 1435 ax-17 1459 ax-i9 1463 |
This theorem depends on definitions: df-bi 115 df-sb 1686 |
This theorem is referenced by: ax16 1734 sbequi 1760 sb5rf 1773 |
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