Theorem sb1 858

Description: One direction of a simplified definition of substitution.

Assertion

Ref	Expression
sb1	⊢ ([y / x]φ → ∃x(x = y ∧ φ))

Proof of Theorem sb1

Step	Hyp	Ref	Expression
1		df-sb 853	. 2 ⊢ ([y / x]φ ↔ ((x = y → φ) ∧ ∃x(x = y ∧ φ)))
2	1	pm3.27bd 263	1 ⊢ ([y / x]φ → ∃x(x = y ∧ φ))

Syntax hints:   → wi 2   ∧ wa 196  ∃wex 678   = weq 797  [wsb 852

This theorem is referenced by:  sb4 861  sbf 870  hbs1f 874  sbn1 880  sbied 903

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-sb 853

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