Theorem axc16g 1940

Description: Generalization of axc16 1941. Use the latter when sufficient. (Contributed by NM, 15-May-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 18-Feb-2018.) Remove dependency on ax-13 1999, along an idea of BJ. (Revised by Wolf Lammen, 30-Nov-2019.)

Assertion

Ref	Expression
axc16g

Distinct variable group:   ,

Proof of Theorem axc16g

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		aevlem1 1939	. 2
2		ax-5 1704	. 2
3		axc112 1937	. 2
4	1, 2, 3	syl2im 38	1

Syntax hints:  ->wi 4  A.wal 1393

This theorem is referenced by:  axc16  1941  ax16gb  1942  aev  1943  aevOLD  2062  ax16nfALT  2065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613