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Theorem pm2.61da2ne 2595
 Description: Deduction eliminating two inequalities in an antecedent. (Contributed by NM, 29-May-2013.)
Hypotheses
Ref Expression
pm2.61da2ne.1 ((φ A = B) → ψ)
pm2.61da2ne.2 ((φ C = D) → ψ)
pm2.61da2ne.3 ((φ (AB CD)) → ψ)
Assertion
Ref Expression
pm2.61da2ne (φψ)

Proof of Theorem pm2.61da2ne
StepHypRef Expression
1 pm2.61da2ne.1 . 2 ((φ A = B) → ψ)
2 pm2.61da2ne.2 . . . 4 ((φ C = D) → ψ)
32adantlr 695 . . 3 (((φ AB) C = D) → ψ)
4 pm2.61da2ne.3 . . . 4 ((φ (AB CD)) → ψ)
54anassrs 629 . . 3 (((φ AB) CD) → ψ)
63, 5pm2.61dane 2594 . 2 ((φ AB) → ψ)
71, 6pm2.61dane 2594 1 (φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642   ≠ wne 2516 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  df-ne 2518 This theorem is referenced by:  pm2.61da3ne  2596
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