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

Step	Hyp	Ref	Expression
1		axc112 2030	. 2 |- ( A. y y = x -> ( A. x ph -> A. y ph ) )
2	1	bj-aecomsv 31393	1 |- ( A. x x = y -> ( A. x ph -> A. y ph ) )

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