Theorem ceqsalg 3134

Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. For an alternate proof, see ceqsalgALT 3135. (Contributed by NM, 29-Oct-2003.) (Proof shortened by BJ, 29-Sep-2019.)

Hypotheses

Ref	Expression
ceqsalg.1
ceqsalg.2

Assertion

Ref	Expression
ceqsalg

Distinct variable group:   ,

Proof of Theorem ceqsalg

Step	Hyp	Ref	Expression
1		ceqsalg.1	. 2
2		ceqsalg.2	. . 3
3	2	ax-gen 1618	. 2
4		ceqsalt 3132	. 2
5	1, 3, 4	mp3an12 1314	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818

This theorem is referenced by:  ceqsal  3136  uniiunlem  3587  ralrnmpt2  6417  sucprcregOLD  8047  fimaxre3  10517  pmapglbx  35493

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-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111