Theorem mpancom 528

Description: An inference based on modus ponens with commutation of antecedents.

Hypotheses

Ref	Expression
mpancom.1	⊢ (ψ → φ)
mpancom.2	⊢ ((φ ∧ ψ) → χ)

Assertion

Ref	Expression
mpancom	⊢ (ψ → χ)

Proof of Theorem mpancom

Step	Hyp	Ref	Expression
1		mpancom.1	. 2 ⊢ (ψ → φ)
2		mpancom.2	. . 3 ⊢ ((φ ∧ ψ) → χ)
3	2	ancoms 334	. 2 ⊢ ((ψ ∧ φ) → χ)
4	1, 3	mpdan 527	1 ⊢ (ψ → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  reuuni3 1958  orduniorsuc 2337  cardnn 3631  ondomcard 3663  ltexprlem4 3939  flidt 4627

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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