Theorem iuneq2i 2584

Description: Equality inference for indexed union.

Hypothesis

Ref	Expression
iuneq2i.1	|- (x e. A -> B = C)

Assertion

Ref	Expression
iuneq2i	|- U_x e. A B = U_x e. A C

Proof of Theorem iuneq2i

Step	Hyp	Ref	Expression
1		iuneq2 2582	. 2 |- (A.x e. A B = C -> U_x e. A B = U_x e. A C)
2		iuneq2i.1	. 2 |- (x e. A -> B = C)
3	1, 2	mprg 1703	1 |- U_x e. A B = U_x e. A C

Syntax hints:   -> wi 3   = wceq 958   e. wcel 960  U_ciun 2570

This theorem is referenced by:  iunab 2601  dfimafn2 3768  funiunfv 3872  abianfplem 3967  r1lim 4663  iundom 4822  alephlim 4875  subtop 7643

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-ral 1652  df-rex 1653  df-v 1815  df-in 2054  df-ss 2056  df-iun 2572

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