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Axiom ax-10o 1645
Description: Axiom ax-10o 1645 ("o" for "old") was the original version of ax-10 1437, before it was discovered (in May 2008) that the shorter ax-10 1437 could replace it. It appears as Axiom scheme C11' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is redundant, as shown by theorem ax10o 1644.

Normally, ax10o 1644 should be used rather than ax-10o 1645, except by theorems specifically studying the latter's properties. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-10o  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)

Detailed syntax breakdown of Axiom ax-10o
StepHypRef Expression
1 vx . . . 4  setvar  x
2 vy . . . 4  setvar  y
31, 2weq 1433 . . 3  wff  x  =  y
43, 1wal 1283 . 2  wff  A. x  x  =  y
5 wph . . . 4  wff  ph
65, 1wal 1283 . . 3  wff  A. x ph
75, 2wal 1283 . . 3  wff  A. y ph
86, 7wi 4 . 2  wff  ( A. x ph  ->  A. y ph )
94, 8wi 4 1  wff  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)
Colors of variables: wff set class
This axiom is referenced by:  ax10  1646
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