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Theorem 2thd 164
Description: Two truths are equivalent (deduction rule). (Contributed by NM, 3-Jun-2012.) (Revised by NM, 29-Jan-2013.)
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 162 . 2 (ψ → (χ → (ψχ)))
41, 2, 3sylc 56 1 (φ → (ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  abvor0dc  3219  euotd  3965  nn0eln0  4268  elabrex  5322  riota5f  5416
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