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Theorem mpancom 650
Description: An inference based on modus ponens with commutation of antecedents. (Contributed by NM, 28-Oct-2003.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpancom.1 (ψφ)
mpancom.2 ((φ ψ) → χ)
Assertion
Ref Expression
mpancom (ψχ)

Proof of Theorem mpancom
StepHypRef Expression
1 mpancom.1 . 2 (ψφ)
2 id 19 . 2 (ψψ)
3 mpancom.2 . 2 ((φ ψ) → χ)
41, 2, 3syl2anc 642 1 (ψχ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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-an 360
This theorem is referenced by:  mpan  651  spesbc  3127  nnc3n3p1  6278  nnc3n3p2  6279  nnc3p1n3p2  6280
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