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Theorem drex1 1967
 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
dral1.1 (x x = y → (φψ))
Assertion
Ref Expression
drex1 (x x = y → (xφyψ))

Proof of Theorem drex1
StepHypRef Expression
1 dral1.1 . . . . 5 (x x = y → (φψ))
21notbid 285 . . . 4 (x x = y → (¬ φ ↔ ¬ ψ))
32dral1 1965 . . 3 (x x = y → (x ¬ φy ¬ ψ))
43notbid 285 . 2 (x x = y → (¬ x ¬ φ ↔ ¬ y ¬ ψ))
5 df-ex 1542 . 2 (xφ ↔ ¬ x ¬ φ)
6 df-ex 1542 . 2 (yψ ↔ ¬ y ¬ ψ)
74, 5, 63bitr4g 279 1 (x x = y → (xφyψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  exdistrf  1971  drsb1  2022  eujustALT  2207  copsexg  4607  dfid3  4768
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