Theorem unieqd 3903

Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.)

Hypothesis

Ref	Expression
unieqd.1	|- (ph -> A = B)

Assertion

Ref	Expression
unieqd	|- (ph -> U.A = U.B)

Proof of Theorem unieqd

Step	Hyp	Ref	Expression
1		unieqd.1	. 2 |- (ph -> A = B)
2		unieq 3901	. 2 |- (A = B -> U.A = U.B)
3	1, 2	syl 15	1 |- (ph -> U.A = U.B)

Syntax hints:   -> wi 4   = wceq 1642  U.cuni 3892

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rex 2621  df-uni 3893

This theorem is referenced by:  uniprg  3907  unisng  3909  iotaeq  4348  iotabi  4349  uniabio  4350  iotanul  4355  dfiota4  4373  elxp4  5109  funfv  5376  fvun  5379  fvco2  5383  fniunfv  5467