Theorem ixpeq2dv 7505

Description: Equality theorem for infinite Cartesian product. (Contributed by Mario Carneiro, 11-Jun-2016.)

Hypothesis

Ref	Expression
ixpeq2dv.1

Assertion

Ref	Expression
ixpeq2dv

Distinct variable group:   ,

Proof of Theorem ixpeq2dv

Step	Hyp	Ref	Expression
1		ixpeq2dv.1	. . 3
2	1	adantr 465	. 2
3	2	ixpeq2dva 7504	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  X_cixp 7489

This theorem is referenced by:  prdsval  14852  brssc  15183  isfunc  15233  natfval  15315  isnat  15316  dprdval  17034  dprdvalOLD  17036  elpt  20073  elptr  20074  dfac14  20119

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-in 3482  df-ss 3489  df-ixp 7490