Theorem eximal 1615

Description: A utility theorem. An interesting case is when the same formula is substituted for both and , since then both implications express a type of non-freeness. See also alimex 1652. (Contributed by BJ, 12-May-2019.)

Assertion

Ref	Expression
eximal

Proof of Theorem eximal

Step	Hyp	Ref	Expression
1		df-ex 1613	. . 3
2	1	imbi1i 325	. 2
3		con1b 333	. 2
4	2, 3	bitri 249	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612

This theorem is referenced by:  ax5e  1706  xfree2  27364  bj-nalnalimiOLD  34223  bj-exalimi  34225

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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