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Theorem drex2 1617
 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 1603 . 2 (x x = yzx x = y)
2 drex2.1 . 2 (x x = y → (φψ))
31, 2exbidh 1502 1 (x x = y → (zφzψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  ∃wex 1378 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  exdistrfor  1678
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