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Mirrors > Home > MPE Home > Th. List > stdpc6 | Structured version Visualization version GIF version |
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1908.) Axiom 6 of [Mendelson] p. 95. Mendelson doesn't say why he prepended the redundant quantifier, but it was probably to be compatible with free logic (which is valid in the empty domain). (Contributed by NM, 16-Feb-2005.) |
Ref | Expression |
---|---|
stdpc6 | ⊢ ∀𝑥 𝑥 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1889 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | 1 | ax-gen 1700 | 1 ⊢ ∀𝑥 𝑥 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1472 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1700 ax-4 1713 ax-5 1793 ax-6 1838 ax-7 1885 |
This theorem depends on definitions: df-bi 195 df-ex 1695 |
This theorem is referenced by: (None) |
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