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Theorem cbvmo 2241
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 9-Mar-1995.) (Revised by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
cbvmo.1 yφ
cbvmo.2 xψ
cbvmo.3 (x = y → (φψ))
Assertion
Ref Expression
cbvmo (∃*xφ∃*yψ)

Proof of Theorem cbvmo
StepHypRef Expression
1 cbvmo.1 . . . 4 yφ
2 cbvmo.2 . . . 4 xψ
3 cbvmo.3 . . . 4 (x = y → (φψ))
41, 2, 3cbvex 1985 . . 3 (xφyψ)
51, 2, 3cbveu 2224 . . 3 (∃!xφ∃!yψ)
64, 5imbi12i 316 . 2 ((xφ∃!xφ) ↔ (yψ∃!yψ))
7 df-mo 2209 . 2 (∃*xφ ↔ (xφ∃!xφ))
8 df-mo 2209 . 2 (∃*yψ ↔ (yψ∃!yψ))
96, 7, 83bitr4i 268 1 (∃*xφ∃*yψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wex 1541  Ⅎwnf 1544  ∃!weu 2204  ∃*wmo 2205 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 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-eu 2208  df-mo 2209 This theorem is referenced by:  dffun6f  5123
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