Theorem axfrege58b 37214

Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2341. Justification for ax-frege58b 37215. (Contributed by RP, 28-Mar-2020.)

Assertion

Ref	Expression
axfrege58b	⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

Proof of Theorem axfrege58b

Step	Hyp	Ref	Expression
1		stdpc4 2341	1 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

Syntax hints:   → wi 4  ∀wal 1473  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868

This theorem is referenced by: (None)