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Theorem mtp-xorOLD 1537
 Description: Obsolete version of mtp-xor 1536 as of 11-Nov-2017. (Contributed by David A. Wheeler, 4-Jul-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
mtp-xor.1 ¬ φ
mtp-xor.2 (φψ)
Assertion
Ref Expression
mtp-xorOLD ψ

Proof of Theorem mtp-xorOLD
StepHypRef Expression
1 mtp-xor.1 . 2 ¬ φ
2 mtp-xor.2 . . . . 5 (φψ)
3 df-xor 1305 . . . . 5 ((φψ) ↔ ¬ (φψ))
42, 3mpbi 199 . . . 4 ¬ (φψ)
5 bicom 191 . . . 4 ((φψ) ↔ (ψφ))
64, 5mtbi 289 . . 3 ¬ (ψφ)
7 xor3 346 . . 3 (¬ (ψφ) ↔ (ψ ↔ ¬ φ))
86, 7mpbi 199 . 2 (ψ ↔ ¬ φ)
91, 8mpbir 200 1 ψ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 176   ⊻ wxo 1304 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 177  df-xor 1305 This theorem is referenced by: (None)
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