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Theorem syl2anr 464
Description: A double syllogism inference. (Contributed by NM, 17-Sep-2013.)
Hypotheses
Ref Expression
syl2an.1 (φψ)
syl2an.2 (τχ)
syl2an.3 ((ψ χ) → θ)
Assertion
Ref Expression
syl2anr ((τ φ) → θ)

Proof of Theorem syl2anr
StepHypRef Expression
1 syl2an.1 . . 3 (φψ)
2 syl2an.2 . . 3 (τχ)
3 syl2an.3 . . 3 ((ψ χ) → θ)
41, 2, 3syl2an 463 . 2 ((φ τ) → θ)
54ancoms 439 1 ((τ φ) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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-an 360
This theorem is referenced by:  funco  5142  resdif  5306  enmap2lem5  6067  sbthlem3  6205
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