Theorem cbvexd 2026

Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2079. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.)

Hypotheses

Ref	Expression
cbvald.1
cbvald.2
cbvald.3

Assertion

Ref	Expression
cbvexd

Distinct variable groups:   ,   ,

Proof of Theorem cbvexd

Step	Hyp	Ref	Expression
1		cbvald.1	. . . 4
2		cbvald.2	. . . . 5
3	2	nfnd 1902	. . . 4
4		cbvald.3	. . . . 5
5		notbi 295	. . . . 5
6	4, 5	syl6ib 226	. . . 4
7	1, 3, 6	cbvald 2025	. . 3
8	7	notbid 294	. 2
9		df-ex 1613	. 2
10		df-ex 1613	. 2
11	8, 9, 10	3bitr4g 288	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616

This theorem is referenced by:  cbvexdva  2033  vtoclgft  3157  dfid3  4801  axrepndlem2  8989  axunnd  8992  axpowndlem2  8994  axpowndlem2OLD  8995  axpownd  8999  axregndlem2  9001  axinfndlem1  9004  axacndlem4  9009  wl-mo2dnae  30019  wl-mo2t  30020

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-11 1842  ax-12 1854  ax-13 1999

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