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Theorem drex2 1602
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)
Hypothesis
Ref Expression
drex2.1 (x x = y → (φψ))
Assertion
Ref Expression
drex2 (x x = y → (zφzψ))

Proof of Theorem drex2
StepHypRef Expression
1 hbae 1588 . 2 (x x = yzx x = y)
2 drex2.1 . 2 (x x = y → (φψ))
31, 2exbidh 1487 1 (x x = y → (zφzψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1226  wex 1362
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-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  exdistrfor  1663
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