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Theorem equequ1OLD 1685
Description: Obsolete version of equequ1 1684 as of 12-Nov-2017. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
equequ1OLD (x = y → (x = zy = z))

Proof of Theorem equequ1OLD
StepHypRef Expression
1 ax-8 1675 . 2 (x = y → (x = zy = z))
2 equcomi 1679 . . 3 (x = yy = x)
3 ax-8 1675 . . 3 (y = x → (y = zx = z))
42, 3syl 15 . 2 (x = y → (y = zx = z))
51, 4impbid 183 1 (x = y → (x = zy = z))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by: (None)
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