Theorem equs5e 1979

Description: A property related to substitution that unlike equs5 2092 doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.) (Proof shortened by Wolf Lammen, 15-Jan-2018.)

Assertion

Ref	Expression
equs5e

Proof of Theorem equs5e

Step	Hyp	Ref	Expression
1		nfa1 1897	. 2
2		hbe1 1839	. . . . 5
3	2	19.23bi 1871	. . . 4
4		ax-12 1854	. . . 4
5	3, 4	syl5 32	. . 3
6	5	imp 429	. 2
7	1, 6	exlimi 1912	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612

This theorem is referenced by:  sb4e  1998

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-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617