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Theorem 2thd 231
Description: Two truths are equivalent (deduction rule). (Contributed by NM, 3-Jun-2012.)
Hypotheses
Ref Expression
2thd.1 (φψ)
2thd.2 (φχ)
Assertion
Ref Expression
2thd (φ → (ψχ))

Proof of Theorem 2thd
StepHypRef Expression
1 2thd.1 . 2 (φψ)
2 2thd.2 . 2 (φχ)
3 pm5.1im 229 . 2 (ψ → (χ → (ψχ)))
41, 2, 3sylc 56 1 (φ → (ψχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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
This theorem is referenced by:  had1  1402  sbc2or  3054  abvor0  3567  ralidm  3653  fcnvres  5243
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