Theorem axc16nfALT 2323

Description: Alternate proof of axc16nf 2137, shorter but requiring ax-11 2034 and ax-13 2246. (Contributed by Mario Carneiro, 7-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc16nfALT	|- ( A. x x = y -> F/ z ph )

Distinct variable group:   x, y

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

Proof of Theorem axc16nfALT

Step	Hyp	Ref	Expression
1		nfae 2316	. 2 |- F/ z A. x x = y
2		axc16g 2134	. 2 |- ( A. x x = y -> ( ph -> A. z ph ) )
3	1, 2	nf5d 2118	1 |- ( A. x x = y -> F/ z ph )

Syntax hints:   -> wi 4   A.wal 1481   F/wnf 1708

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-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)