Theorem pssned 3933

Description: Proper subclasses are unequal. Deduction form of pssne 3931. (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 3931	. 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝐴 ≠ 𝐵)

Syntax hints:   → wi 4   ≠ wne 2999   ⊊ wpss 3799

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 199  df-an 387  df-pss 3814

This theorem is referenced by:  ackbij1lem15  9378  canthnumlem  9792  canthp1lem2  9797  mrieqv2d  16659  slwpss  18385  topdifinffinlem  33735  lsatssn0  35072  islshpcv  35123  lkrpssN  35233