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Theorem spimev 1714
Description: Distinct-variable version of spime 1602. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spimev.1 (x = y → (φψ))
Assertion
Ref Expression
spimev (φxψ)
Distinct variable group:   φ,x
Allowed substitution hints:   φ(y)   ψ(x,y)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1394 . 2 xφ
2 spimev.1 . 2 (x = y → (φψ))
31, 2spime 1602 1 (φxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1354
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 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323
This theorem is referenced by:  speiv  1715  rnxpid  4670
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