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Theorem syl13anc 1136
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1 (φψ)
sylXanc.2 (φχ)
sylXanc.3 (φθ)
sylXanc.4 (φτ)
syl13anc.5 ((ψ (χ θ τ)) → η)
Assertion
Ref Expression
syl13anc (φη)

Proof of Theorem syl13anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . . 3 (φχ)
3 sylXanc.3 . . 3 (φθ)
4 sylXanc.4 . . 3 (φτ)
52, 3, 43jca 1083 . 2 (φ → (χ θ τ))
6 syl13anc.5 . 2 ((ψ (χ θ τ)) → η)
71, 5, 6syl2anc 391 1 (φη)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by:  syl23anc  1141  syl33anc  1149  caovassd  5602  caovcand  5605  caovordid  5609  caovordd  5611  caovdid  5618  caovdird  5621  swoer  6070  swoord1  6071  swoord2  6072  prarloclem3  6479  fzosubel3  8782
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