Theorem bj-axc16g16 32674

Description: Proof of axc16g 2134 from { ax-1 6-- ax-7 1935, axc16 2135 }. (Contributed by BJ, 6-Jul-2021.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-axc16g16	|- ( A. x x = y -> ( ph -> A. z ph ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y, z)

Proof of Theorem bj-axc16g16

Dummy variable t is distinct from all other variables.

Step	Hyp	Ref	Expression
1		aevlem 1981	. 2 |- ( A. x x = y -> A. z z = t )
2		axc16 2135	. 2 |- ( A. z z = t -> ( ph -> A. z ph ) )
3	1, 2	syl 17	1 |- ( A. x x = y -> ( ph -> A. z 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: (None)