Theorem spesbcd 3072

Description: form of spsbc 2997. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
spesbcd.1	⊢ (𝜑 → [𝐴 / 𝑥]𝜓)

Assertion

Ref	Expression
spesbcd	⊢ (𝜑 → ∃𝑥𝜓)

Proof of Theorem spesbcd

Step	Hyp	Ref	Expression
1		spesbcd.1	. 2 ⊢ (𝜑 → [𝐴 / 𝑥]𝜓)
2		spesbc 3071	. 2 ⊢ ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∃wex 1503  [wsbc 2985

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-v 2762  df-sbc 2986

This theorem is referenced by:  euotd  4283  bj-sels  15351