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Theorem ax5eq 2262
Description: Theorem to add distinct quantifier to atomic formula. (This theorem demonstrates the induction basis for ax-5 1704 considered as a metatheorem. Do not use it for later proofs - use ax-5 1704 instead, to avoid reference to the redundant axiom ax-c16 2223.) (Contributed by NM, 10-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax5eq
Distinct variable groups:   ,   ,

Proof of Theorem ax5eq
StepHypRef Expression
1 ax-c9 2221 . 2
2 ax-c16 2223 . 2
3 ax-c16 2223 . 2
41, 2, 3pm2.61ii 165 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
This theorem is referenced by:  dveeq1-o16  2266
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-c9 2221  ax-c16 2223
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