Theorem equsal 2036

Description: A useful equivalence related to substitution. (Contributed by NM, 2-Jun-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 5-Feb-2018.)

Hypotheses

Ref	Expression
equsal.1
equsal.2

Assertion

Ref	Expression
equsal

Proof of Theorem equsal

Step	Hyp	Ref	Expression
1		equsal.1	. . 3
2	1	19.23 1910	. 2
3		equsal.2	. . . 4
4	3	pm5.74i 245	. . 3
5	4	albii 1640	. 2
6		ax6e 2002	. . 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  F/wnf 1616

This theorem is referenced by:  equsalh  2037  equsex  2038  axc9lem2  2040  dvelimf  2076  sb6x  2125  sb6rf  2166  asymref2  5389  intirr  5390  fun11  5658  pm13.192  31317

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  ax-13 1999

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