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Theorem ax17el 2189
Description: Theorem to add distinct quantifier to atomic formula. This theorem demonstrates the induction basis for ax-17 1616 considered as a metatheorem.) (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax17el (x yz x y)
Distinct variable groups:   x,z   y,z

Proof of Theorem ax17el
StepHypRef Expression
1 ax-15 2143 . 2 z z = x → (¬ z z = y → (x yz x y)))
2 ax-16 2144 . 2 (z z = x → (x yz x y))
3 ax-16 2144 . 2 (z z = y → (x yz x y))
41, 2, 3pm2.61ii 157 1 (x yz x y)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-15 2143  ax-16 2144
This theorem is referenced by:  dveel2ALT  2191
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