Theorem unieqi 1928

Description: Inference of equality of two class unions.

Hypothesis

Ref	Expression
unieqi.1	⊢ A = B

Assertion

Ref	Expression
unieqi	⊢ ∪A = ∪B

Proof of Theorem unieqi

Step	Hyp	Ref	Expression
1		unieqi.1	. 2 ⊢ A = B
2		unieq 1927	. 2 ⊢ (A = B → ∪A = ∪B)
3	1, 2	ax-mp 6	1 ⊢ ∪A = ∪B

Syntax hints:   = wceq 1091  ∪cuni 1919

This theorem is referenced by:  unop 1931  unisn 1932  unidif0 1944  reuuni1 1955  reucl 1957  reuuni3 1958  univ 1964  supex 2157  unisuc 2299  op1sta 2635  op2nda 2639  fv2 2828  tfrlem8 2956  tfrlem9 2957  tz7.44-2 2967  tz7.44-3 2968  ecqs 3233  xpassen 3344  unir1 3511  aceq5lem2 3559  kmlem10 3589  hta 3619

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-uni 1920

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