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Theorem bj-axc11v 31395
Description: Version of axc11 2158 with a dv condition, which does not require ax-13 2101. Remark: the following theorems (hbae 2159, nfae 2160, hbnae 2161, nfnae 2162, hbnaes 2163) would need to be totally unbundled to be proved without ax-13 2101, hence would be simple consequences of ax-5 1768 or nfv 1771. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-axc11v  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem bj-axc11v
StepHypRef Expression
1 axc112 2030 . 2  |-  ( A. y  y  =  x  ->  ( A. x ph  ->  A. y ph )
)
21bj-aecomsv 31393 1  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674
This theorem is referenced by:  bj-axc16g  31397  bj-dral1v  31402
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