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Mirrors > Home > ILE Home > Th. List > ax-11 | Unicode version |
Description: Axiom of Variable
Substitution. One of the 5 equality axioms of predicate
calculus. The final consequent
is a way of
expressing "
substituted for in wff
" (cf. sb6 1858).
It
is based on Lemma 16 of [Tarski] p. 70 and
Axiom C8 of [Monk2] p. 105,
from which it can be proved by cases.
Variants of this axiom which are equivalent in classical logic but which have not been shown to be equivalent for intuitionistic logic are ax11v 1799, ax11v2 1792 and ax-11o 1795. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ax-11 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx | . . 3 | |
2 | vy | . . 3 | |
3 | 1, 2 | weq 1479 | . 2 |
4 | wph | . . . 4 | |
5 | 4, 2 | wal 1329 | . . 3 |
6 | 3, 4 | wi 4 | . . . 4 |
7 | 6, 1 | wal 1329 | . . 3 |
8 | 5, 7 | wi 4 | . 2 |
9 | 3, 8 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: ax10o 1693 equs5a 1766 sbcof2 1782 ax11o 1794 ax11v 1799 |
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