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Theorem sylancom 397
Description: Syllogism inference with commutation of antecents. (Contributed by NM, 2-Jul-2008.)
Hypotheses
Ref Expression
sylancom.1 ((φ ψ) → χ)
sylancom.2 ((χ ψ) → θ)
Assertion
Ref Expression
sylancom ((φ ψ) → θ)

Proof of Theorem sylancom
StepHypRef Expression
1 sylancom.1 . 2 ((φ ψ) → χ)
2 simpr 103 . 2 ((φ ψ) → ψ)
3 sylancom.2 . 2 ((χ ψ) → θ)
41, 2, 3syl2anc 391 1 ((φ ψ) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  ordin  4088  fimacnvdisj  5017  fvimacnv  5225  recgt1i  7605  avgle2  7903  ioodisj  8591  fzneuz  8693
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