Theorem pssned 3368

Description: Proper subclasses are unequal. Deduction form of pssne 3366. (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 3366	. 2 ⊢ (A ⊊ B → A ≠ B)
3	1, 2	syl 15	1 ⊢ (φ → A ≠ B)

Syntax hints:   → wi 4   ≠ wne 2517   ⊊ wpss 3259

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-pss 3262

This theorem is referenced by: (None)