Theorem bj-axc16b 31459

Description: Remove dependency on ax-13 2102 from axc16b 4612. (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-axc16b	|- ( A. x x = y -> ( ph -> A. x ph ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-axc16b

Step	Hyp	Ref	Expression
1		bj-dtru 31458	. 2 |- -. A. x x = y
2	1	pm2.21i 136	1 |- ( A. x x = y -> ( ph -> A. x ph ) )

Syntax hints:   -> wi 4   A.wal 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-8 1900  ax-9 1907  ax-10 1926  ax-11 1931  ax-12 1944  ax-nul 4550  ax-pow 4598

This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679

This theorem is referenced by: (None)