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Theorem sblimv 1771
Description: Version of sblim 1828 where x and y are distinct. (Contributed by Jim Kingdon, 19-Jan-2018.)
Hypothesis
Ref Expression
sblimv.1 (ψxψ)
Assertion
Ref Expression
sblimv ([y / x](φψ) ↔ ([y / x]φψ))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   ψ(x,y)

Proof of Theorem sblimv
StepHypRef Expression
1 sbimv 1770 . 2 ([y / x](φψ) ↔ ([y / x]φ → [y / x]ψ))
2 sblimv.1 . . . 4 (ψxψ)
32sbh 1656 . . 3 ([y / x]ψψ)
43imbi2i 215 . 2 (([y / x]φ → [y / x]ψ) ↔ ([y / x]φψ))
51, 4bitri 173 1 ([y / x](φψ) ↔ ([y / x]φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240  [wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by: (None)
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