Theorem pssned 3705

Description: Proper subclasses are unequal. Deduction form of pssne 3703. (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 3703	. 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ≠ 𝐵)

Syntax hints:   → wi 4   ≠ wne 2794   ⊊ wpss 3575

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 386  df-pss 3590

This theorem is referenced by:  ackbij1lem15  9056  canthnumlem  9470  canthp1lem2  9475  mrieqv2d  16299  slwpss  18027  topdifinffinlem  33195  lsatssn0  34289  islshpcv  34340  lkrpssN  34450