Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1879).
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 1820, ax11v2 1813 and ax-11o 1816. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ax-11 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx | . . 3 | |
2 | vy | . . 3 | |
3 | 1, 2 | weq 1496 | . 2 |
4 | wph | . . . 4 | |
5 | 4, 2 | wal 1346 | . . 3 |
6 | 3, 4 | wi 4 | . . . 4 |
7 | 6, 1 | wal 1346 | . . 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 1708 equs5a 1787 sbcof2 1803 ax11o 1815 ax11v 1820 |
Copyright terms: Public domain | W3C validator |