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Axiom ax-i11e 1390
Description: Axiom of Variable Substitution for Existence. This can be derived from ax-11 1389 in a classical context but a separate axiom is needed for intuitionistic predicate calculus.
Assertion
Ref Expression
ax-i11e (x = y → (yφx(x = y φ)))

Detailed syntax breakdown of Axiom ax-i11e
StepHypRef Expression
1 vx . . 3 set x
2 vy . . 3 set y
31, 2weq 1384 . 2 wff x = y
4 wph . . . 4 wff φ
54, 2wex 1374 . . 3 wff yφ
63, 4wa 96 . . . 4 wff (x = y φ)
76, 1wex 1374 . . 3 wff x(x = y φ)
85, 7wi 4 . 2 wff (yφx(x = y φ))
93, 8wi 4 1 wff (x = y → (yφx(x = y φ)))
Colors of variables: wff set class
This axiom is referenced by:  drex1  1588
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