Theorem bj-axc11v 32747

Description: Version of axc11 2314 with a dv condition, which does not require ax-13 2246 nor ax-10 2019. Remark: the following theorems (hbae 2315, nfae 2316, hbnae 2317, nfnae 2318, hbnaes 2319) would need to be totally unbundled to be proved without ax-13 2246, hence would be simple consequences of ax-5 1839 or nfv 1843. (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		axc11r 2187	. 2 |- ( A. y y = x -> ( A. x ph -> A. y ph ) )
2	1	bj-aecomsv 32746	1 |- ( A. x x = y -> ( A. x ph -> A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  bj-dral1v  32748