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Axiom ax-c11 32378
Description: Axiom ax-c11 32378 was the original version of ax-c11n 32379 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 32379 could replace it. It appears as Axiom scheme C11' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is obsolete and should no longer be used. It is proved above as theorem axc11 2109. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c11  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)

Detailed syntax breakdown of Axiom ax-c11
StepHypRef Expression
1 vx . . . 4  setvar  x
2 vy . . . 4  setvar  y
31, 2weq 1780 . . 3  wff  x  =  y
43, 1wal 1435 . 2  wff  A. x  x  =  y
5 wph . . . 4  wff  ph
65, 1wal 1435 . . 3  wff  A. x ph
75, 2wal 1435 . . 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 setvar class
This axiom is referenced by:  aecom-o  32390  hbae-o  32392  dral1-o  32393  axc11nfromc11  32416  dvelimf-o  32419
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