Theorem equsalhw 1945

Description: Weaker version of equsalh 2037 (requiring distinct variables) without using ax-13 1999. (Contributed by NM, 29-Nov-2015.) (Proof shortened by Wolf Lammen, 28-Dec-2017.)

Hypotheses

Ref	Expression
equsalhw.1
equsalhw.2

Assertion

Ref	Expression
equsalhw

Distinct variable group:   ,

Proof of Theorem equsalhw

Step	Hyp	Ref	Expression
1		equsalhw.1	. . 3
2	1	19.23h 1911	. 2
3		equsalhw.2	. . . 4
4	3	pm5.74i 245	. . 3
5	4	albii 1640	. 2
6		ax6ev 1749	. . 3
7	6	a1bi 337	. 2
8	2, 5, 7	3bitr4i 277	1

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

This theorem is referenced by:  dvelimhw  1955

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-ex 1613  df-nf 1617