Theorem pssned 3856

Description: Proper subclasses are unequal. Deduction form of pssne 3854. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
pssssd.1	⊢ (𝜑 → 𝐴 ⊊ 𝐵)

Assertion

Ref	Expression
pssned	⊢ (𝜑 → 𝐴 ≠ 𝐵)

Proof of Theorem pssned

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 ⊢ (𝜑 → 𝐴 ⊊ 𝐵)
2		pssne 3854	. 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ≠ 𝐵)

Syntax hints:   → wi 4   ≠ wne 2943   ⊊ wpss 3725

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 197  df-an 383  df-pss 3740

This theorem is referenced by:  ackbij1lem15  9259  canthnumlem  9673  canthp1lem2  9678  mrieqv2d  16508  slwpss  18235  topdifinffinlem  33533  lsatssn0  34812  islshpcv  34863  lkrpssN  34973