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Theorem merco2 1501
 Description: A single axiom for propositional calculus offered by Meredith. This axiom has 19 symbols, sans auxiliaries. See notes in merco1 1478. (Contributed by Anthony Hart, 7-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco2 (((φψ) → (( ⊥ → χ) → θ)) → ((θφ) → (τ → (ηφ))))

Proof of Theorem merco2
StepHypRef Expression
1 falim 1328 . . . . . 6 ( ⊥ → χ)
2 pm2.04 76 . . . . . 6 (((φψ) → (( ⊥ → χ) → θ)) → (( ⊥ → χ) → ((φψ) → θ)))
31, 2mpi 16 . . . . 5 (((φψ) → (( ⊥ → χ) → θ)) → ((φψ) → θ))
4 jarl 155 . . . . . 6 (((φψ) → θ) → (¬ φθ))
5 idd 21 . . . . . 6 (((φψ) → θ) → (θθ))
64, 5jad 154 . . . . 5 (((φψ) → θ) → ((φθ) → θ))
7 looinv 174 . . . . 5 (((φθ) → θ) → ((θφ) → φ))
83, 6, 73syl 18 . . . 4 (((φψ) → (( ⊥ → χ) → θ)) → ((θφ) → φ))
98a1dd 42 . . 3 (((φψ) → (( ⊥ → χ) → θ)) → ((θφ) → (τφ)))
109a1i 10 . 2 (η → (((φψ) → (( ⊥ → χ) → θ)) → ((θφ) → (τφ))))
1110com4l 78 1 (((φψ) → (( ⊥ → χ) → θ)) → ((θφ) → (τ → (ηφ))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊥ wfal 1317 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320 This theorem is referenced by:  mercolem1  1502  mercolem2  1503  mercolem3  1504  mercolem4  1505  mercolem5  1506  mercolem6  1507  mercolem7  1508  mercolem8  1509  re1tbw4  1513
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