Theorem iuneq1i 39259

Description: Equality theorem for indexed union. (Contributed by Glauco Siliprandi, 3-Mar-2021.)

Hypothesis

Ref	Expression
iuneq1i.1	|- A = B

Assertion

Ref	Expression
iuneq1i	|- U_ x e. A C = U_ x e. B C

Distinct variable groups:   x, A   x, B

Allowed substitution hint:   C( x)

Proof of Theorem iuneq1i

Step	Hyp	Ref	Expression
1		iuneq1i.1	. 2 |- A = B
2		iuneq1 4534	. 2 |- ( A = B -> U_ x e. A C = U_ x e. B C )
3	1, 2	ax-mp 5	1 |- U_ x e. A C = U_ x e. B C

Syntax hints:   = wceq 1483   U_ciun 4520

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-v 3202  df-in 3581  df-ss 3588  df-iun 4522

This theorem is referenced by:  ovolval4lem1  40863